multiprocessing async .get() hangs if the pool is terminated

Bug report

Bug description:

MWE

Steps to reproduce:

import multiprocessing
from time import sleep

with multiprocessing.Pool() as p:
    result = p.apply_async(sleep, (1,))
result.get()

Expected behavior:

Either:

• result is returned. (Pool().__exit__ waits for every async task to finish); or
• some kind of exception is raised when .get() is called outside with Pool()

Comments

This is the same as #79659. That was marked as completed in 2021. However it seems the issue is still present.

CPython versions tested on:

3.12, 3.13, 3.14

Operating systems tested on:

Linux

Start by running the provided MWE and tracing the interaction between Pool.exit and the asynchronous result's .get() call after the pool is terminated. Compare the behavior with issue #79659 and add coverage for the documented expected outcome: completion or an exception instead of a hang.