diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 1e42b15363fb36..41f1c52bc42288 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -140,8 +140,8 @@ function ReadableState(options, stream, isDuplex) {
   // Has it been destroyed
   this.destroyed = false;
 
-  // Indicates whether the stream has errored.
-  this.errored = false;
+  // Indicates whether the stream has errored. Contains the error.
+  this.errored = null;
 
   // Crypto is kind of old and crusty.  Historically, its default string
   // encoding is 'binary' so we have to make this configurable.
diff --git a/lib/_stream_writable.js b/lib/_stream_writable.js
index 7753eaf1f1c674..7f0974fbb41602 100644
--- a/lib/_stream_writable.js
+++ b/lib/_stream_writable.js
@@ -171,7 +171,8 @@ function WritableState(options, stream, isDuplex) {
   // Indicates whether the stream has errored. When true all write() calls
   // should return false. This is needed since when autoDestroy
   // is disabled we need a way to tell whether the stream has failed.
-  this.errored = false;
+  // Contains the error.
+  this.errored = null;
 
   // Count buffered requests
   this.bufferedRequestCount = 0;
@@ -488,7 +489,12 @@ function onwrite(stream, er) {
   state.writelen = 0;
 
   if (er) {
-    state.errored = true;
+    if (!state.errored) {
+      state.errored = er;
+    }
+    if (stream._readableState && !stream._readableState.errored) {
+      stream._readableState.errored = er;
+    }
     if (sync) {
       process.nextTick(onwriteError, stream, state, er, cb);
     } else {
diff --git a/lib/internal/streams/destroy.js b/lib/internal/streams/destroy.js
index fb206c6c83d0a0..2e50ca9d1a70d8 100644
--- a/lib/internal/streams/destroy.js
+++ b/lib/internal/streams/destroy.js
@@ -8,21 +8,19 @@ function destroy(err, cb) {
   const w = this._writableState;
 
   if (err) {
-    if (w) {
-      w.errored = true;
+    if (w && !w.errored) {
+      w.errored = err;
     }
-    if (r) {
-      r.errored = true;
+    if (r && !r.errored) {
+      r.errored = err;
     }
   }
 
   if ((w && w.destroyed) || (r && r.destroyed)) {
     if (cb) {
-      cb(err);
-    } else if (err) {
-      process.nextTick(emitErrorNT, this, err);
+      // TODO(ronag): Wait until 'close' is emitted (if not already emitted).
+      cb((w && w.errored) || (r && r.errored));
     }
-
     return this;
   }
 
@@ -38,32 +36,30 @@ function destroy(err, cb) {
 
   this._destroy(err || null, (err) => {
     if (err) {
-      if (w) {
-        w.errored = true;
+      if (w && !w.errored) {
+        w.errored = err;
       }
-      if (r) {
-        r.errored = true;
+      if (r && !r.errored) {
+        r.errored = err;
       }
     }
 
     if (cb) {
       // Invoke callback before scheduling emitClose so that callback
       // can schedule before.
-      cb(err);
+      cb((w && w.errored) || (r && r.errored));
       // Don't emit 'error' if passed a callback.
       process.nextTick(emitCloseNT, this);
-    } else if (err) {
-      process.nextTick(emitErrorCloseNT, this, err);
     } else {
-      process.nextTick(emitCloseNT, this);
+      process.nextTick(emitErrorCloseNT, this);
     }
   });
 
   return this;
 }
 
-function emitErrorCloseNT(self, err) {
-  emitErrorNT(self, err);
+function emitErrorCloseNT(self) {
+  emitErrorNT(self);
   emitCloseNT(self);
 }
 
@@ -76,10 +72,16 @@ function emitCloseNT(self) {
   }
 }
 
-function emitErrorNT(self, err) {
+function emitErrorNT(self) {
   const r = self._readableState;
   const w = self._writableState;
 
+  const err = (w && w.errored) || (r && r.errored);
+
+  if (!err) {
+    return;
+  }
+
   if ((w && w.errorEmitted) || (r && r.errorEmitted)) {
     return;
   }
@@ -100,7 +102,7 @@ function undestroy() {
 
   if (r) {
     r.destroyed = false;
-    r.errored = false;
+    r.errored = null;
     r.reading = false;
     r.ended = false;
     r.endEmitted = false;
@@ -109,7 +111,7 @@ function undestroy() {
 
   if (w) {
     w.destroyed = false;
-    w.errored = false;
+    w.errored = null;
     w.ended = false;
     w.ending = false;
     w.finalCalled = false;
@@ -132,13 +134,13 @@ function errorOrDestroy(stream, err) {
   if ((r && r.autoDestroy) || (w && w.autoDestroy))
     stream.destroy(err);
   else if (err) {
-    if (w) {
-      w.errored = true;
+    if (w && !w.errored) {
+      w.errored = err;
     }
-    if (r) {
-      r.errored = true;
+    if (r && !r.errored) {
+      r.errored = err;
     }
-    emitErrorNT(stream, err);
+    emitErrorNT(stream);
   }
 }
 
diff --git a/test/parallel/test-stream-auto-destroy.js b/test/parallel/test-stream-auto-destroy.js
index 2a1a5190debb57..22ca09bccaeb5f 100644
--- a/test/parallel/test-stream-auto-destroy.js
+++ b/test/parallel/test-stream-auto-destroy.js
@@ -86,13 +86,14 @@ const assert = require('assert');
 {
   const r = new stream.Readable({
     read() {
-      r2.emit('error', new Error('fail'));
+      r2.destroy(new Error('fail'));
     }
   });
   const r2 = new stream.Readable({
     autoDestroy: true,
     destroy: common.mustCall((err, cb) => cb())
   });
+  r2.on('error', common.mustCall());
 
   r.pipe(r2);
 }
@@ -100,13 +101,14 @@ const assert = require('assert');
 {
   const r = new stream.Readable({
     read() {
-      w.emit('error', new Error('fail'));
+      w.destroy(new Error('fail'));
     }
   });
   const w = new stream.Writable({
     autoDestroy: true,
     destroy: common.mustCall((err, cb) => cb())
   });
+  w.on('error', common.mustCall());
 
   r.pipe(w);
 }
diff --git a/test/parallel/test-stream-duplex-destroy.js b/test/parallel/test-stream-duplex-destroy.js
index 3c38d2c364051c..5c9b0937078e5e 100644
--- a/test/parallel/test-stream-duplex-destroy.js
+++ b/test/parallel/test-stream-duplex-destroy.js
@@ -76,8 +76,8 @@ const assert = require('assert');
   duplex.on('end', common.mustNotCall('no end event'));
   duplex.on('finish', common.mustNotCall('no finish event'));
 
-  // Error is swallowed by the custom _destroy
-  duplex.on('error', common.mustNotCall('no error event'));
+  // Error is NOT swallowed by the custom _destroy
+  duplex.on('error', common.mustCall());
   duplex.on('close', common.mustCall());
 
   duplex.destroy(expected);
diff --git a/test/parallel/test-stream-readable-destroy.js b/test/parallel/test-stream-readable-destroy.js
index d446dd3611781e..1ac77d4220c0a7 100644
--- a/test/parallel/test-stream-readable-destroy.js
+++ b/test/parallel/test-stream-readable-destroy.js
@@ -69,8 +69,8 @@ const assert = require('assert');
 
   read.on('end', common.mustNotCall('no end event'));
 
-  // Error is swallowed by the custom _destroy
-  read.on('error', common.mustNotCall('no error event'));
+  // Error is NOT swallowed by the custom _destroy
+  read.on('error', common.mustCall());
   read.on('close', common.mustCall());
 
   read.destroy(expected);
@@ -134,13 +134,13 @@ const assert = require('assert');
   read.on('error', common.mustCall((err) => {
     assert.strictEqual(ticked, true);
     assert.strictEqual(read._readableState.errorEmitted, true);
-    assert.strictEqual(read._readableState.errored, true);
+    assert.strictEqual(read._readableState.errored, expected);
     assert.strictEqual(err, expected);
   }));
 
   read.destroy();
   assert.strictEqual(read._readableState.errorEmitted, false);
-  assert.strictEqual(read._readableState.errored, true);
+  assert.strictEqual(read._readableState.errored, expected);
   assert.strictEqual(read.destroyed, true);
   ticked = true;
 }
@@ -190,15 +190,15 @@ const assert = require('assert');
   // destroy(err, callback);
   read.on('error', common.mustNotCall());
 
-  assert.strictEqual(read._readableState.errored, false);
+  assert.strictEqual(read._readableState.errored, null);
   assert.strictEqual(read._readableState.errorEmitted, false);
 
   read.destroy(expected, common.mustCall(function(err) {
-    assert.strictEqual(read._readableState.errored, true);
+    assert.strictEqual(read._readableState.errored, expected);
     assert.strictEqual(err, expected);
   }));
   assert.strictEqual(read._readableState.errorEmitted, false);
-  assert.strictEqual(read._readableState.errored, true);
+  assert.strictEqual(read._readableState.errored, expected);
   ticked = true;
 }
 
@@ -223,14 +223,15 @@ const assert = require('assert');
 
   readable.destroy();
   assert.strictEqual(readable.destroyed, true);
-  assert.strictEqual(readable._readableState.errored, false);
+  assert.strictEqual(readable._readableState.errored, null);
   assert.strictEqual(readable._readableState.errorEmitted, false);
 
   // Test case where `readable.destroy()` is called again with an error before
   // the `_destroy()` callback is called.
-  readable.destroy(new Error('kaboom 2'));
+  const expected = new Error('kaboom 2');
+  readable.destroy(expected);
   assert.strictEqual(readable._readableState.errorEmitted, false);
-  assert.strictEqual(readable._readableState.errored, true);
+  assert.strictEqual(readable._readableState.errored, expected);
 
   ticked = true;
 }
diff --git a/test/parallel/test-stream-transform-destroy.js b/test/parallel/test-stream-transform-destroy.js
index c594d9989ae4de..38764ebe0fb92b 100644
--- a/test/parallel/test-stream-transform-destroy.js
+++ b/test/parallel/test-stream-transform-destroy.js
@@ -72,8 +72,8 @@ const assert = require('assert');
   transform.on('close', common.mustCall());
   transform.on('finish', common.mustNotCall('no finish event'));
 
-  // Error is swallowed by the custom _destroy
-  transform.on('error', common.mustNotCall('no error event'));
+  // Error is NOT swallowed by the custom _destroy
+  transform.on('error', common.mustCall());
 
   transform.destroy(expected);
 }
diff --git a/test/parallel/test-stream-writable-destroy.js b/test/parallel/test-stream-writable-destroy.js
index d321d808199d56..6bbb04fbbb4c40 100644
--- a/test/parallel/test-stream-writable-destroy.js
+++ b/test/parallel/test-stream-writable-destroy.js
@@ -83,8 +83,33 @@ const assert = require('assert');
   write.on('finish', common.mustNotCall('no finish event'));
   write.on('close', common.mustCall());
 
-  // Error is swallowed by the custom _destroy
-  write.on('error', common.mustNotCall('no error event'));
+  // Error is NOT swallowed by the custom _destroy
+  write.on('error', common.mustCall((err) => {
+    assert.strictEqual(err, expected);
+  }));
+
+  write.destroy(expected);
+  assert.strictEqual(write.destroyed, true);
+}
+
+{
+  const write = new Writable({
+    write(chunk, enc, cb) { cb(); },
+    destroy: common.mustCall(function(err, cb) {
+      assert.strictEqual(err, expected);
+      cb(new Error('not this error'));
+    })
+  });
+
+  const expected = new Error('kaboom');
+
+  write.on('finish', common.mustNotCall('no finish event'));
+  write.on('close', common.mustCall());
+
+  // Error is NOT overriden by the custom _destroy
+  write.on('error', common.mustCall((err) => {
+    assert.strictEqual(err, expected);
+  }));
 
   write.destroy(expected);
   assert.strictEqual(write.destroyed, true);
@@ -167,9 +192,10 @@ const assert = require('assert');
     assert.strictEqual(write._writableState.errorEmitted, true);
   }));
 
-  write.destroy(new Error('kaboom 1'));
+  const expected = new Error('kaboom 1');
+  write.destroy(expected);
   write.destroy(new Error('kaboom 2'));
-  assert.strictEqual(write._writableState.errored, true);
+  assert.strictEqual(write._writableState.errored, expected);
   assert.strictEqual(write._writableState.errorEmitted, false);
   assert.strictEqual(write.destroyed, true);
   ticked = true;
@@ -198,14 +224,15 @@ const assert = require('assert');
 
   writable.destroy();
   assert.strictEqual(writable.destroyed, true);
-  assert.strictEqual(writable._writableState.errored, false);
+  assert.strictEqual(writable._writableState.errored, null);
   assert.strictEqual(writable._writableState.errorEmitted, false);
 
   // Test case where `writable.destroy()` is called again with an error before
   // the `_destroy()` callback is called.
-  writable.destroy(new Error('kaboom 2'));
+  const expected = new Error('kaboom 2');
+  writable.destroy(expected);
   assert.strictEqual(writable._writableState.errorEmitted, false);
-  assert.strictEqual(writable._writableState.errored, true);
+  assert.strictEqual(writable._writableState.errored, expected);
 
   ticked = true;
 }
@@ -249,6 +276,9 @@ const assert = require('assert');
   write.destroy(expected, common.mustCall(function(err) {
     assert.strictEqual(err, expected);
   }));
+  write.on('error', common.mustCall((err) => {
+    assert.strictEqual(err, expected);
+  }));
 }
 
 {