"No. But actually I think that people abandoning things for too long in the communal fridge is a bigger problem than people using things that aren't theirs,"
Funny that you should mention that, I once found a pasta salad way in the back. It was so old that it had completely dried out. I moved it to the front and put a note on it for the owner to deal with it. It was still there days later, so I threw bowl and all away. It was a nice bowl too, obviously part of an expensive set.
A month later, there was another pasta salad, in the process of drying out, also in the back of the fridge. Once again I moved it to the front, this time with a note stating that bowl and all would be tossed out (like the last one) if the owner didn't deal with it. The next day it was gone and I never saw a pasta salad in that fridge again.
When I first started at my previous job, each person would take a turn at going to one or more restaurants and bringing back food for everyone. Most of the time they also brought back packets of condiments and any left over packets would go into a drawer in the fridge. Since it was impossible to tell how old a packet was, nobody ever used them. The fridge hadn't been cleaned out in so long that there was scummy water in the bottom and somthing sticky running down the back wall. It took me 4 hours to clean that thing out, it was so messy. And, I threw away all of the old packets of condiments too. The next day, one of my coworkers wanted some mayo and couldn't find any. But at least the fridge was still nice and clean.