diff --git a/lib/internal/webstreams/readablestream.js b/lib/internal/webstreams/readablestream.js
index 8e27bae439f8e3..80e02379edab6b 100644
--- a/lib/internal/webstreams/readablestream.js
+++ b/lib/internal/webstreams/readablestream.js
@@ -589,18 +589,24 @@ class ReadableStream {
         'DataCloneError');
     }
 
+    const { port1, port2 } = this[kState].transfer;
+
+    this[kState].transfer.port2 = undefined;
+
+    const transfer = lazyTransfer();
     const {
       writable,
+      source,
       promise,
-    } = lazyTransfer().newCrossRealmWritableSink(
-      this,
-      this[kState].transfer.port1);
+    } = transfer.newCrossRealmWritableSink(this, port1);
+
+    transfer.closeRegistry().register(port2, source);
 
     this[kState].transfer.writable = writable;
     this[kState].transfer.promise = promise;
 
     return {
-      data: { port: this[kState].transfer.port2 },
+      data: { port: port2 },
       deserializeInfo:
         'internal/webstreams/readablestream:TransferredReadableStream',
     };
diff --git a/lib/internal/webstreams/transfer.js b/lib/internal/webstreams/transfer.js
index 136b0d81a99464..f016b73e9f8cbd 100644
--- a/lib/internal/webstreams/transfer.js
+++ b/lib/internal/webstreams/transfer.js
@@ -4,6 +4,7 @@ const {
   ObjectDefineProperties,
   PromiseResolve,
   ReflectConstruct,
+  SafeFinalizationRegistry,
 } = primordials;
 
 const {
@@ -261,10 +262,18 @@ class CrossRealmTransformWritableSink {
   }
 }
 
+let finalizer = null;
+
+function closeRegistry() {
+  return (finalizer ??= new SafeFinalizationRegistry((source) => {
+    source[kState].port.close();
+  }));
+}
+
 function newCrossRealmReadableStream(writable, port) {
-  const readable =
-    new ReadableStream(
-      new CrossRealmTransformReadableSource(port));
+  const source = new CrossRealmTransformReadableSource(port);
+
+  const readable = new ReadableStream(source);
 
   const promise =
     readableStreamPipeTo(readable, writable, false, false, false);
@@ -273,19 +282,21 @@ function newCrossRealmReadableStream(writable, port) {
 
   return {
     readable,
+    source,
     promise,
   };
 }
 
 function newCrossRealmWritableSink(readable, port) {
-  const writable =
-    new WritableStream(
-      new CrossRealmTransformWritableSink(port));
+  const source = new CrossRealmTransformWritableSink(port);
+
+  const writable = new WritableStream(source);
 
   const promise = readableStreamPipeTo(readable, writable, false, false, false);
   setPromiseHandled(promise);
   return {
     writable,
+    source,
     promise,
   };
 }
@@ -297,4 +308,5 @@ module.exports = {
   CrossRealmTransformReadableSource,
   CloneableDOMException,
   InternalCloneableDOMException,
+  closeRegistry,
 };
diff --git a/lib/internal/webstreams/writablestream.js b/lib/internal/webstreams/writablestream.js
index 2115aba36e927b..4bd5e03363649a 100644
--- a/lib/internal/webstreams/writablestream.js
+++ b/lib/internal/webstreams/writablestream.js
@@ -282,20 +282,27 @@ class WritableStream {
         'DataCloneError');
     }
 
+    const { port1, port2 } = this[kState].transfer;
+
+    this[kState].transfer.port2 = undefined;
+
+    const transfer = lazyTransfer();
     const {
       readable,
+      source,
       promise,
-    } = lazyTransfer().newCrossRealmReadableStream(
+    } = transfer.newCrossRealmReadableStream(
       this,
-      this[kState].transfer.port1);
+      port1);
+
+    transfer.closeRegistry().register(port2, source);
 
     this[kState].transfer.readable = readable;
     this[kState].transfer.promise = promise;
 
-    setPromiseHandled(this[kState].transfer.promise);
 
     return {
-      data: { port: this[kState].transfer.port2 },
+      data: { port: port2 },
       deserializeInfo:
         'internal/webstreams/writablestream:TransferredWritableStream',
     };
diff --git a/test/parallel/test-webstreams-using-structuredclone-exit-process.js b/test/parallel/test-webstreams-using-structuredclone-exit-process.js
new file mode 100644
index 00000000000000..7018c2d34445fb
--- /dev/null
+++ b/test/parallel/test-webstreams-using-structuredclone-exit-process.js
@@ -0,0 +1,32 @@
+'use strict';
+
+const common = require('../common');
+const { Worker } = require('worker_threads');
+const { once } = require('node:events');
+
+const worker = new Worker(
+  `
+  const { ReadableStream } = require('stream/web');
+  const rs = new ReadableStream();
+  const cloned = structuredClone(rs, { transfer: [rs] });
+  `,
+  { eval: true },
+);
+
+const worker2 = new Worker(
+  `
+  const { WritableStream } = require('stream/web');
+  const ws = new WritableStream();
+  const cloned = structuredClone(ws, { transfer: [ws] });
+  `,
+  { eval: true },
+);
+
+(async () => {
+  // A timer is used here to detect the end of a process.
+  const timer = setTimeout(common.mustNotCall(), common.platformTimeout(10000));
+
+  await Promise.all([once(worker, 'exit'), once(worker2, 'exit')]);
+
+  clearTimeout(timer);
+})().then(common.mustCall());