diff --git a/.changeset/clean-kings-like.md b/.changeset/clean-kings-like.md
new file mode 100644
index 0000000..89cb926
--- /dev/null
+++ b/.changeset/clean-kings-like.md
@@ -0,0 +1,5 @@
+---
+'fetch-nodeshim': patch
+---
+
+Limit state in which `incoming.socket` is unrefed and instead `.ref()` it when the body is being read, and `.unref()` it again when reading stops.
diff --git a/src/fetch.ts b/src/fetch.ts
index 6fefc12..96c5277 100644
--- a/src/fetch.ts
+++ b/src/fetch.ts
@@ -1,4 +1,5 @@
 import { Stream, Readable, pipeline } from 'node:stream';
+import { Socket } from 'node:net';
 import * as https from 'node:https';
 import * as http from 'node:http';
 import * as url from 'node:url';
@@ -112,6 +113,18 @@ function createResponse(
   return response;
 }
 
+function attachRefLifetime(body: Readable, socket: Socket): void {
+  const { _read } = body;
+  body.on('close', () => {
+    socket.unref();
+  });
+  body._read = function _readRef(...args: Parameters<Readable['_read']>) {
+    body._read = _read;
+    socket.ref();
+    return _read.apply(this, args);
+  };
+}
+
 async function _fetch(
   input: string | URL | Request,
   requestInit?: RequestInit
@@ -257,6 +270,12 @@ async function _fetch(
         outgoing.on('error', destroy);
       }
 
+      // Re-ref the socket when the body starts being consumed to prevent
+      // early process exit, then unref when done to allow normal exit.
+      if (body != null) {
+        attachRefLifetime(body, incoming.socket);
+      }
+
       resolve(
         createResponse(body, init, {
           type: 'default',