In Germany (also highly depends on county/city) yes, they do normally fare pretty well and shelters often operate multiple feeding stations where there are a lot of strays. So they get to know the „local strays“ and can keep an eye on them via volunteers and cams.

When a cat is visibly sick, they catch them at this station, treat them and if the cat is alright, oftentimes release them again - shelters are notoriously full and money ist scarce for these organisations unfortunately…

However, if there are conditions that make life for this cat (or others - e.g. FIV) dangerous, they are normally kept in the shelter and then opened for adoption as a „only indoors cat“.

Also, older cats often end up in shelters because they often belonged to older people - and when they can’t care for the cats anymore, have to move or die one day, the cats have to go somewhere too.