diff --git a/lib/internal/streams/end-of-stream.js b/lib/internal/streams/end-of-stream.js
index 1753996a4f85de..32c2a983a4c082 100644
--- a/lib/internal/streams/end-of-stream.js
+++ b/lib/internal/streams/end-of-stream.js
@@ -13,6 +13,15 @@ function isRequest(stream) {
   return stream.setHeader && typeof stream.abort === 'function';
 }
 
+function isStreamEmittingClose(stream) {
+  if (stream._writableState && !stream._writableState.emitClose)
+    return false;
+  if (stream._readableState && !stream._readableState.emitClose)
+    return false;
+
+  return true;
+}
+
 function eos(stream, opts, callback) {
   if (arguments.length === 2) {
     callback = opts;
@@ -71,6 +80,18 @@ function eos(stream, opts, callback) {
     stream.req.on('finish', onfinish);
   };
 
+  const isEmittingClose = isStreamEmittingClose(stream);
+
+  if (!isEmittingClose) {
+    const _destroy = stream._destroy;
+    stream._destroy = function(err, cb) {
+      _destroy.call(stream, err, (_err) => {
+        if (!_err) process.nextTick(() => callback.call(stream, _err));
+        cb(_err);
+      });
+    };
+  }
+
   if (isRequest(stream)) {
     stream.on('complete', onfinish);
     stream.on('abort', onclose);
diff --git a/test/parallel/test-stream-finished.js b/test/parallel/test-stream-finished.js
index fe87f246327a3a..8672b7b3892cee 100644
--- a/test/parallel/test-stream-finished.js
+++ b/test/parallel/test-stream-finished.js
@@ -5,6 +5,7 @@ const { Writable, Readable, Transform, finished } = require('stream');
 const assert = require('assert');
 const fs = require('fs');
 const { promisify } = require('util');
+const Countdown = require('../common/countdown');
 
 {
   const rs = new Readable({
@@ -175,3 +176,52 @@ const { promisify } = require('util');
   rs.push(null);
   rs.resume();
 }
+
+{
+  const rs = new Readable({
+    emitClose: false,
+    read() {}
+  });
+
+  finished(rs, common.mustCall((err) => {
+    assert(!err, 'no error');
+  }));
+
+  setImmediate(() => rs.destroy());
+}
+
+{
+  const ws = new Writable({
+    emitClose: false,
+    write(data, enc, cb) {
+      cb();
+    }
+  });
+
+  finished(ws, common.mustCall((err) => {
+    assert(!err, 'no error');
+  }));
+
+  setImmediate(() => ws.destroy());
+}
+
+{
+  const countdown = new Countdown(1, common.mustCall());
+  const rs = new Readable({
+    emitClose: false,
+    read() {},
+    destroy(err, cb) {
+      setImmediate(() => {
+        countdown.dec();
+        cb(err);
+      });
+    }
+  });
+
+  finished(rs, common.mustCall((err) => {
+    assert(!err, 'no error');
+    assert(!countdown.remaining, 'destroy should be called first');
+  }));
+
+  setImmediate(() => rs.destroy());
+}
diff --git a/test/parallel/test-stream-pipeline.js b/test/parallel/test-stream-pipeline.js
index ef5a39fddd881f..d078e868832004 100644
--- a/test/parallel/test-stream-pipeline.js
+++ b/test/parallel/test-stream-pipeline.js
@@ -5,6 +5,7 @@ const { Stream, Writable, Readable, Transform, pipeline } = require('stream');
 const assert = require('assert');
 const http = require('http');
 const { promisify } = require('util');
+const Countdown = require('../common/countdown');
 
 {
   let finished = false;
@@ -477,3 +478,49 @@ const { promisify } = require('util');
     { code: 'ERR_INVALID_CALLBACK' }
   );
 }
+
+{
+  const read = new Readable({
+    read() {}
+  });
+
+  const write = new Writable({
+    emitClose: false,
+    write(data, enc, cb) {
+      cb();
+    }
+  });
+
+  setImmediate(() => read.destroy());
+
+  pipeline(read, write, common.mustCall((err) => {
+    assert.ok(err, 'should have an error');
+  }));
+}
+
+{
+  const countdown = new Countdown(1, common.mustCall());
+  const read = new Readable({
+    read() {}
+  });
+
+  const write = new Writable({
+    emitClose: false,
+    write(data, enc, cb) {
+      cb();
+    },
+    destroy(err, cb) {
+      setImmediate(() => {
+        countdown.dec();
+        cb(err);
+      });
+    }
+  });
+
+  setImmediate(() => read.destroy());
+
+  pipeline(read, write, common.mustCall((err) => {
+    assert.ok(err, 'should have an error');
+    assert(!countdown.remaining, 'destroy should be called first');
+  }));
+}