How will astronomers know when the universe stops expanding?
They don't know.
The expansion of the universe is regulated by gravity and something that we do not know and we call Dark Energy.
The DA is accelerating the expansion of the universe and, until we do not understand what DE is, we will not be able to make predictions about the fate of the expansion.
It can expand forever or stop, at a certain moment. Right now nobody knows.
The supernova studies of 1997, 1998 were done to confirm the hypothesis that the universe would stop expanding. The theory that matter and energy were eternal and would recycle between Big Bangs and Big Crushes required that rate of expansion should slow down and eventually reverse.
The studies indicated that the rate of expansion of the universe is actually increases not decreasing as predicted. The implications are that the universe will never stop expanding, the universe is an open system, matter and energy are not eternal, nor self existent.
The astronomers would know if universe is stopping to expand by studying the rates of expansion. These studies which have been done indicates the universe will not stop expanding