Thanks so much for looking into this, Serhiy!

> 2. StopAsyncIteration is dynamically looked up in globals. If set the global StopAsyncIteration or delete it from builtins (for example at the shutdown stage), this will break any "async for".

IIRC I adapted the approach from some other place in compile.c. Quick looking at it reveals that the `assert` statement is compiled in a similar way w.r.t. how AssertionError is looked up at runtime.  You might want to check if there are other places in compile.c that need to be fixed.

> PR 6052 fixes issue 1. I don't know what is the best place for tests. There are two files with tests for "async for": test_coroutines.py and test_asyncgen.py. I'm not sure that new tests use the simplest way for testing this behavior. Could you please look at them Yury?

I think the new tests are fine.