diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index fc0baca1b81235..a466011b682beb 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -66,7 +66,6 @@ ObjectSetPrototypeOf(Readable.prototype, Stream.prototype);
 ObjectSetPrototypeOf(Readable, Stream);
 
 const { errorOrDestroy } = destroyImpl;
-const kProxyEvents = ['error', 'close', 'destroy', 'pause', 'resume'];
 
 function prependListener(emitter, event, fn) {
   // Sadly this is not cacheable as some libraries bundle their own
@@ -1034,10 +1033,29 @@ Readable.prototype.wrap = function(stream) {
     }
   }
 
-  // Proxy certain important events.
-  for (const kProxyEvent of kProxyEvents) {
-    stream.on(kProxyEvent, this.emit.bind(this, kProxyEvent));
-  }
+  stream.on('error', (err) => {
+    errorOrDestroy(this, err);
+  });
+
+  stream.on('close', () => {
+    // TODO(ronag): Update readable state?
+    this.emit('close');
+  });
+
+  stream.on('destroy', () => {
+    // TODO(ronag): this.destroy()?
+    this.emit('destroy');
+  });
+
+  stream.on('pause', () => {
+    // TODO(ronag): this.pause()?
+    this.emit('pause');
+  });
+
+  stream.on('resume', () => {
+    // TODO(ronag): this.resume()?
+    this.emit('resume');
+  });
 
   // When we try to consume some more bytes, simply unpause the
   // underlying stream.
diff --git a/test/parallel/test-stream2-readable-wrap-error.js b/test/parallel/test-stream2-readable-wrap-error.js
new file mode 100644
index 00000000000000..b56b9bc41c7527
--- /dev/null
+++ b/test/parallel/test-stream2-readable-wrap-error.js
@@ -0,0 +1,32 @@
+'use strict';
+const common = require('../common');
+const assert = require('assert');
+
+const Readable = require('_stream_readable');
+const EE = require('events').EventEmitter;
+
+const oldStream = new EE();
+oldStream.pause = () => {};
+oldStream.resume = () => {};
+
+{
+  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.destroyed, true);
+    }));
+  oldStream.emit('error', 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.destroyed, false);
+    }));
+  oldStream.emit('error', new Error());
+}