[v13.x backport] stream: avoid destroying writable source

lib/internal/streams/pipeline.js

@@ -37,6 +37,11 @@ function destroyer(stream, reading, writing, final, callback) {
   eos(stream, { readable: reading, writable: writing }, (err) => {
     if (destroyed) return;
     destroyed = true;
+
+    if (!err && reading && !writing && stream.writable) {
+      return callback();
+    }
+
     const readable = stream.readable || isRequest(stream);
     if (err || !final || !readable) {
       destroyImpl.destroyer(stream, err);

test/parallel/test-stream-pipeline.js

@@ -995,3 +995,19 @@ const { promisify } = require('util');
     assert.strictEqual(res, '');
   }));
 }
+
+{
+  // Might still want to be able to use the writable side
+  // of src. This is in the case where e.g. the Duplex input
+  // is not directly connected to its output. Such a case could
+  // happen when the Duplex is reading from a socket and then echos
+  // the data back on the same socket.
+  const src = new PassThrough();
+  assert.strictEqual(src.writable, true);
+  const dst = new PassThrough();
+  pipeline(src, dst, common.mustCall((err) => {
+    assert.strictEqual(src.writable, true);
+    assert.strictEqual(src.destroyed, false);
+  }));
+  src.push(null);
+}