I found out today! They rot! I thought they just got black spots on them and were stinky.
I've been searching for DD's new bathing suit and haven't seen it since we got back from Costa Rica (in February!). It was inside a plastic grocery bag of wet clothes that she left inside a zippered pocket of her suitcase when she unpacked. Now I've left wet clothes in the washer a few times and had them get a little stinky, but I've never (in 66 years!) had a full-blown case of mildew before.
I washed everything in Tide with Bleach Alternative, and the cotton stuff came out in shreds. The bathing suit is nylon and it seems to be OK. Due to the pattern, if it has black spots, they don't show. No stink, either. Before I send the suit to Boise with DD, I'm going to have her put it on to be sure it doesn't explode!