Not carrying migration card
What happens if the police asks for your migration card and you don't have it with you?
I'm asking out of curiosity, but here is some context:
I am a Mexican (Mexican-looking man) traveling within Russia with my girlfriend (she is Mexican, but a lot of people think that she is Asian).
(In Moscow) A friend of mine invited us to dinner. After dinner, she walked with us to the metro station, but suddenly a police car stopped by us and two policemen (with a gun in their hands) got out.
They asked for our documents. We presented our passports, but they asked for our migration cards. Of course we had them with us. They read them, and then said that everything was ok and left.
I knew that, given we were carrying our documents, everything would be fine, but my girlfriend freaked out, since it was the first time in her life that she was stopped by the police. So, we are wondering... what would have happened if precisely today we had forgotten our passports/migration cards in the hotel?
Thanks in advance.