diff --git a/packages/pg-cloudflare/src/index.ts b/packages/pg-cloudflare/src/index.ts
index 527b433f5..366752d1e 100644
--- a/packages/pg-cloudflare/src/index.ts
+++ b/packages/pg-cloudflare/src/index.ts
@@ -163,7 +163,15 @@ export class CloudflareSocket extends EventEmitter {
           this._upgraded = true
         }
       })
-      .catch((e) => this.emit('error', e))
+      .catch((e) => {
+        // workerd can reject `closed` with `undefined`
+        this.emit('error', e ?? new Error('Socket closed with an error'))
+        // like net.Socket, follow the error with 'close' so the connection ends
+        if (this._cfSocket === socket) {
+          this._cfSocket = null
+          this.emit('close')
+        }
+      })
   }
 }
 
diff --git a/packages/pg-esm-test/pg-cloudflare.test.js b/packages/pg-esm-test/pg-cloudflare.test.js
index 683229158..6c53f50e7 100644
--- a/packages/pg-esm-test/pg-cloudflare.test.js
+++ b/packages/pg-esm-test/pg-cloudflare.test.js
@@ -19,6 +19,29 @@ describe('pg-cloudflare', () => {
     assert.doesNotThrow(() => socket.end())
   })
 
+  it('should emit error then close when the closed promise rejects', async () => {
+    const socket = new CloudflareSocket()
+    const underlyingSocket = { closed: Promise.reject(undefined) }
+    socket._cfSocket = underlyingSocket
+
+    const events = []
+    socket.on('error', (error) => events.push(error))
+    await new Promise((resolve, reject) => {
+      const timer = setTimeout(() => reject(new Error('close event was not emitted')), 100)
+      socket.once('close', () => {
+        clearTimeout(timer)
+        events.push('close')
+        resolve()
+      })
+      socket._addClosedHandler()
+    })
+
+    assert.equal(events.length, 2)
+    assert.ok(events[0] instanceof Error)
+    assert.equal(events[1], 'close')
+    assert.equal(socket._cfSocket, null)
+  })
+
   it('should call the write(data, callback) callback exactly once', async () => {
     const socket = new CloudflareSocket()
     socket._cfWriter = { write: () => Promise.resolve() }