Refrigerating mushrooms does extend their shelf life so the mushrooms won't go bad as quick in the refrigerator like they would if left out at room temperature.
But even when refrigerated mushrooms can and do go bad eventually after a few days to a week even when refrigerated.
When mushrooms go bad the mushrooms will develop a sticky/slimy surface and get darker in color which means they are bad and should be thrown out.
The mushrooms may also develop a bad smell to them as well.
You can freeze the mushrooms and they will last from 3 to 6 months and sometimes longer but in the refrigerator the mushrooms will last from a few days to a week at most.