Personally I obviously have never ever done this, but this friend of mine and his friends, throughout the aughts, have had to give trivial bribes to cops a few times. It's like real-life microtransactions. Usually with something like smoking in a non-smoking area as a pretext, the key is that cops would immediately go for the bribe schtik - they would tell him how they now need to bring him to the station to write up the protocol, and probably nobody would bother with such a small thing and they'd just let him go eventually but the mayor or whatever is not there right now, he's out on some assignment, so he'd have to wait for him to return for a couple hours for the protocol to be written up properly, and hey he is from the neighborhood and so he knows the station is actually a 20-minute walk too, completely out of the way, so maybe he can, like, go buy a pack of cigarettes, and as he opens it, absent-mindedly stuff the "change", let's say X, into the pack?.. and then they'd ask him for a smoke as he returns from the store and he gives them the pack and he can go?..
This is just poor student level; I bet others paid much more, Moscow road police were legendary, although I didn't drive so cannot confirm.
That said I think it's a separate issue from unprompted ID checks, although one could facilitate the other.