diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index c15850f9aa2064..af8786198674cb 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -145,8 +145,11 @@ 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. When true no further
+  // _read calls, 'data' or 'readable' events should occur. This is needed
+  // since when autoDestroy is disabled we need a way to tell whether the
+  // stream has failed.
+  this.errored = null;
 
   // Indicates whether the stream has finished destroying.
   this.closed = false;
diff --git a/lib/_stream_writable.js b/lib/_stream_writable.js
index 236e236aa32459..4d42e5cd6b660a 100644
--- a/lib/_stream_writable.js
+++ b/lib/_stream_writable.js
@@ -171,7 +171,7 @@ 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;
+  this.errored = null;
 
   // Indicates whether the stream has finished destroying.
   this.closed = false;
@@ -407,7 +407,19 @@ function onwrite(stream, er) {
   state.writelen = 0;
 
   if (er) {
-    state.errored = true;
+    // Avoid V8 leak, https://github.com/nodejs/node/pull/34103#issuecomment-652002364
+    er.stack;
+
+    if (!state.errored) {
+      state.errored = er;
+    }
+
+    // In case of duplex streams we need to notify the readable side of the
+    // error.
+    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 f7f282ec5079f3..8cb7509ea66aa2 100644
--- a/lib/internal/streams/destroy.js
+++ b/lib/internal/streams/destroy.js
@@ -15,11 +15,14 @@ function destroy(err, cb) {
   }
 
   if (err) {
-    if (w) {
-      w.errored = true;
+    // Avoid V8 leak, https://github.com/nodejs/node/pull/34103#issuecomment-652002364
+    err.stack;
+
+    if (w && !w.errored) {
+      w.errored = err;
     }
-    if (r) {
-      r.errored = true;
+    if (r && !r.errored) {
+      r.errored = err;
     }
   }
 
@@ -35,11 +38,14 @@ function destroy(err, cb) {
 
   this._destroy(err || null, (err) => {
     if (err) {
-      if (w) {
-        w.errored = true;
+      // Avoid V8 leak, https://github.com/nodejs/node/pull/34103#issuecomment-652002364
+      err.stack;
+
+      if (w && !w.errored) {
+        w.errored = err;
       }
-      if (r) {
-        r.errored = true;
+      if (r && !r.errored) {
+        r.errored = err;
       }
     }
 
@@ -108,7 +114,7 @@ function undestroy() {
     r.closed = false;
     r.closeEmitted = false;
     r.destroyed = false;
-    r.errored = false;
+    r.errored = null;
     r.errorEmitted = false;
     r.reading = false;
     r.ended = false;
@@ -118,7 +124,7 @@ function undestroy() {
   if (w) {
     w.closed = false;
     w.destroyed = false;
-    w.errored = false;
+    w.errored = null;
     w.ended = false;
     w.ending = false;
     w.finalCalled = false;
@@ -145,11 +151,14 @@ function errorOrDestroy(stream, err, sync) {
   if ((r && r.autoDestroy) || (w && w.autoDestroy))
     stream.destroy(err);
   else if (err) {
-    if (w) {
-      w.errored = true;
+    // Avoid V8 leak, https://github.com/nodejs/node/pull/34103#issuecomment-652002364
+    err.stack;
+
+    if (w && !w.errored) {
+      w.errored = err;
     }
-    if (r) {
-      r.errored = true;
+    if (r && !r.errored) {
+      r.errored = err;
     }
 
     if (sync) {
diff --git a/test/parallel/test-stream-readable-destroy.js b/test/parallel/test-stream-readable-destroy.js
index 3d1ac8c92f9bd3..8ab78ec8ccec35 100644
--- a/test/parallel/test-stream-readable-destroy.js
+++ b/test/parallel/test-stream-readable-destroy.js
@@ -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');
     assert.strictEqual(err, expected);
   }));
 
-  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 +223,14 @@ 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'));
   assert.strictEqual(readable._readableState.errorEmitted, false);
-  assert.strictEqual(readable._readableState.errored, false);
+  assert.strictEqual(readable._readableState.errored, null);
 
   ticked = true;
 }
@@ -253,3 +253,18 @@ const assert = require('assert');
   assert.strictEqual(read.destroyed, true);
   read.read();
 }
+
+{
+  const read = new Readable({
+    autoDestroy: false,
+    read() {
+      this.push(null);
+      this.push('asd');
+    }
+  });
+
+  read.on('error', common.mustCall(() => {
+    assert(read._readableState.errored);
+  }));
+  read.resume();
+}
diff --git a/test/parallel/test-stream-writable-destroy.js b/test/parallel/test-stream-writable-destroy.js
index 706847a8582d0c..9f6136923ee176 100644
--- a/test/parallel/test-stream-writable-destroy.js
+++ b/test/parallel/test-stream-writable-destroy.js
@@ -167,9 +167,10 @@ 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;
@@ -200,14 +201,14 @@ 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'));
   assert.strictEqual(writable._writableState.errorEmitted, false);
-  assert.strictEqual(writable._writableState.errored, false);
+  assert.strictEqual(writable._writableState.errored, null);
 
   ticked = true;
 }
@@ -401,3 +402,18 @@ const assert = require('assert');
   }));
   write.destroy();
 }
+
+{
+  const write = new Writable({
+    autoDestroy: false,
+    write(chunk, enc, cb) {
+      cb();
+      cb();
+    }
+  });
+
+  write.on('error', common.mustCall(() => {
+    assert(write._writableState.errored);
+  }));
+  write.write('asd');
+}
diff --git a/test/parallel/test-stream2-readable-wrap-error.js b/test/parallel/test-stream2-readable-wrap-error.js
index b56b9bc41c7527..ac1f64f69810f0 100644
--- a/test/parallel/test-stream2-readable-wrap-error.js
+++ b/test/parallel/test-stream2-readable-wrap-error.js
@@ -10,23 +10,25 @@ oldStream.pause = () => {};
 oldStream.resume = () => {};
 
 {
+  const err = new Error();
   const r = new Readable({ autoDestroy: true })
     .wrap(oldStream)
     .on('error', common.mustCall(() => {
       assert.strictEqual(r._readableState.errorEmitted, true);
-      assert.strictEqual(r._readableState.errored, true);
+      assert.strictEqual(r._readableState.errored, err);
       assert.strictEqual(r.destroyed, true);
     }));
-  oldStream.emit('error', new Error());
+  oldStream.emit('error', err);
 }
 
 {
+  const err = new Error();
   const r = new Readable({ autoDestroy: false })
     .wrap(oldStream)
     .on('error', common.mustCall(() => {
       assert.strictEqual(r._readableState.errorEmitted, true);
-      assert.strictEqual(r._readableState.errored, true);
+      assert.strictEqual(r._readableState.errored, err);
       assert.strictEqual(r.destroyed, false);
     }));
-  oldStream.emit('error', new Error());
+  oldStream.emit('error', err);
 }