It's a few years since I last crossed a European border in an international sleeper train... but the arrangement always used to be that one left one's ticket and passport with the attendant who would take care of all the formalities.

I'll never forget the time when we had to get off a train at 5 am and the attendant was fast asleep (with our passports and Interrails locked in his safe), and no amount of shouting at him and shaking him would wake him up. We eventually had to call in the station attendant, who proceeded to thump him... which did the trick.