WritableStreamDefaultWriter.closed

const writableStream = new WritableStream({
  start(controller) {
  },
  write(chunk, controller) {
    ...
  },
  close(controller) {
    ...
  },
  abort(err) {
    ...
  }
}, queuingStrategy);

...

const writer = writableStream.getWriter();

..

// check if the stream is closed
writer.closed.then(() => {
  console.log('writer closed');
})