This just happened:
I was with a group who was riding the light rail home after a few drinks downtown. On the light rail, we noticed a man who was wearing a football jersey but also carrying a bejeweled purse and a bright pink pool cue case (apparently this is a thing, I had never heard of it or seen one before). He eventually pulled out a cell phone from the bag - which had a pink cover on it.
A number of us independently came to the conclusion that this man had robbed a woman downtown and we whispered this suspicion to each other on the train. I had hoped that maybe he was just a genderqueer individual who presented masculine with clothing but preferred feminine accessories. I was alone in this analysis. We tried to think of a few things to do to get this woman her bag back (such as stealing it from him as we ran off the train) but I worried about our safety. Also, we didn't directly observe him stealing the bag so we didn't know for sure that it wasn't his.
We ended up getting off at the same stop as he did. We observed his behavior to see where he went and what he did. We noticed that about a block past the light rail stop, he hunched over in an alley and started looking through the bag. At this point we felt very confident that he stole the bag and was leafing through to see what he could find. We stayed back to see what he did with the bag; if he was going to dump it out and just steal her money, we were going to scoop the bag up and see if there was some way we could get the bag back to the owner. In the end, he took nothing out of the bag but grabbed it and took it with him down the alley.
So I wonder, if you were in our situation, what would you have done? Would you have called the police with no direct evidence of theft? Would you have confronted him? I feel really guilty that we did nothing but I don't know what else we could have done without compromising our own safety. I feel bad for the woman who is bagless tonight :(