diff --git a/lib/internal/streams/destroy.js b/lib/internal/streams/destroy.js
index 0d3eb6327b9d75..27985482cee70b 100644
--- a/lib/internal/streams/destroy.js
+++ b/lib/internal/streams/destroy.js
@@ -48,12 +48,15 @@ function destroy(err, cb) {
   }
 
   this._destroy(err || null, (err) => {
+    const emitClose = (w && w.emitClose) || (r && r.emitClose);
     if (cb) {
-      process.nextTick(emitCloseNT, this);
+      if (emitClose) {
+        process.nextTick(emitCloseNT, this);
+      }
       cb(err);
     } else if (needError(this, err)) {
-      process.nextTick(emitErrorAndCloseNT, this, err);
-    } else {
+      process.nextTick(emitClose ? emitErrorCloseNT : emitErrorNT, this, err);
+    } else if (emitClose) {
       process.nextTick(emitCloseNT, this);
     }
   });
@@ -61,22 +64,19 @@ function destroy(err, cb) {
   return this;
 }
 
-function emitErrorAndCloseNT(self, err) {
-  emitErrorNT(self, err);
-  emitCloseNT(self);
+function emitErrorCloseNT(self, err) {
+  self.emit('error', err);
+  self.emit('close');
 }
 
 function emitCloseNT(self) {
-  const r = self._readableState;
-  const w = self._writableState;
-
-  if (w && !w.emitClose)
-    return;
-  if (r && !r.emitClose)
-    return;
   self.emit('close');
 }
 
+function emitErrorNT(self, err) {
+  self.emit('error', err);
+}
+
 function undestroy() {
   const r = this._readableState;
   const w = this._writableState;
@@ -100,10 +100,6 @@ function undestroy() {
   }
 }
 
-function emitErrorNT(self, err) {
-  self.emit('error', err);
-}
-
 function errorOrDestroy(stream, err) {
   // We have tests that rely on errors being emitted
   // in the same tick, so changing this is semver major.