diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index 6fa3540057be33..73d18b19bb53dc 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -147,6 +147,8 @@ function ReadableState(options, stream, isDuplex) {
   // Indicates whether the stream has errored.
   this.errored = false;
 
+  this.closed = false;
+
   // Crypto is kind of old and crusty.  Historically, its default string
   // encoding is 'binary' so we have to make this configurable.
   // Everything else in the universe uses 'utf8', though.
diff --git a/lib/_stream_writable.js b/lib/_stream_writable.js
index 3f029883705a0a..6d65abebcb030c 100644
--- a/lib/_stream_writable.js
+++ b/lib/_stream_writable.js
@@ -175,6 +175,8 @@ function WritableState(options, stream, isDuplex) {
   // is disabled we need a way to tell whether the stream has failed.
   this.errored = false;
 
+  this.closed = false;
+
   // Count buffered requests
   this.bufferedRequestCount = 0;
 
diff --git a/lib/internal/streams/destroy.js b/lib/internal/streams/destroy.js
index b80fb56a6bf324..3115202ca6bdee 100644
--- a/lib/internal/streams/destroy.js
+++ b/lib/internal/streams/destroy.js
@@ -73,6 +73,13 @@ function emitCloseNT(self) {
   const r = self._readableState;
   const w = self._writableState;
 
+  if (w) {
+    w.closed = true;
+  }
+  if (r) {
+    r.closed = true;
+  }
+
   if ((w && w.emitClose) || (r && r.emitClose)) {
     self.emit('close');
   }
@@ -103,6 +110,7 @@ function undestroy() {
   if (r) {
     r.destroyed = false;
     r.errored = false;
+    r.closed = false;
     r.reading = false;
     r.ended = false;
     r.endEmitted = false;
@@ -112,6 +120,7 @@ function undestroy() {
   if (w) {
     w.destroyed = false;
     w.errored = false;
+    w.closed = false;
     w.ended = false;
     w.ending = false;
     w.finalCalled = false;
diff --git a/lib/internal/streams/end-of-stream.js b/lib/internal/streams/end-of-stream.js
index dd42eb9f5b3f46..0388533dac0167 100644
--- a/lib/internal/streams/end-of-stream.js
+++ b/lib/internal/streams/end-of-stream.js
@@ -44,16 +44,25 @@ function eos(stream, opts, callback) {
     callback.call(stream, err);
   };
 
-  let writableFinished = stream.writableFinished ||
-    (stream._writableState && stream._writableState.finished);
-  let readableEnded = stream.readableEnded ||
-    (stream._readableState && stream._readableState.endEmitted);
+  const w = stream._writableState;
+  const r = stream._readableState;
 
-  if (writableFinished || readableEnded || stream.destroyed ||
-      stream.aborted) {
+  let writableFinished = stream.writableFinished || (w && w.finished);
+  let readableEnded = stream.readableEnded || (r && r.endEmitted);
+
+  const errorEmitted = (w && w.errorEmitted) || (r && r.errorEmitted);
+  const closed = (w && w.closed) || (r && r.closed);
+
+  if (writableFinished || readableEnded || errorEmitted || closed) {
+    // TODO(ronag): rethrow if errorEmitted?
+    // TODO(ronag): premature close if closed but not
+    // errored, finished or ended?
+
+    // Swallow any error past this point.
     if (opts.error !== false) stream.on('error', onerror);
-    // A destroy(err) call emits error in nextTick.
+
     process.nextTick(callback.bind(stream));
+
     return () => {
       stream.removeListener('error', onerror);
     };
diff --git a/test/parallel/test-stream-finished.js b/test/parallel/test-stream-finished.js
index caca55601868a2..b6db7a867606a4 100644
--- a/test/parallel/test-stream-finished.js
+++ b/test/parallel/test-stream-finished.js
@@ -197,10 +197,14 @@ const { promisify } = require('util');
 {
   // Completed if readable-like is ended before.
 
+  let ticked = false;
   const streamLike = new EE();
   streamLike.readableEnded = true;
   streamLike.readable = true;
-  finished(streamLike, common.mustCall());
+  finished(streamLike, common.mustCall(() => {
+    assert.strictEqual(ticked, true);
+  }));
+  ticked = true;
 }
 
 {
@@ -215,42 +219,6 @@ const { promisify } = require('util');
   streamLike.emit('close');
 }
 
-{
-  // Completed if writable-like is destroyed before.
-
-  const streamLike = new EE();
-  streamLike.destroyed = true;
-  streamLike.writable = true;
-  finished(streamLike, common.mustCall());
-}
-
-{
-  // Completed if readable-like is aborted before.
-
-  const streamLike = new EE();
-  streamLike.destroyed = true;
-  streamLike.readable = true;
-  finished(streamLike, common.mustCall());
-}
-
-{
-  // Completed if writable-like is aborted before.
-
-  const streamLike = new EE();
-  streamLike.aborted = true;
-  streamLike.writable = true;
-  finished(streamLike, common.mustCall());
-}
-
-{
-  // Completed if readable-like is aborted before.
-
-  const streamLike = new EE();
-  streamLike.aborted = true;
-  streamLike.readable = true;
-  finished(streamLike, common.mustCall());
-}
-
 {
   // Completed if streamlike is finished before.