I hope the site comes up with a solution, as until then, it looks like the 50 move rule applies, and will someone stop that elephant from trumpeting and doing all sorts of other things in that room.
I just realized even the 50 move rule may not suffice:
Pawns can move and still no way to win.
The 50 move rule suffices. Eventually. In that position it may be 299 moves later if both players try to prolong it.
Even top engines can't understand positions like this. I had a wonderful blitz game where I trapped an opponent's bishop and analysing it afterwards the engine got it wrong with enormous amounts of computing time. It thought the 100% trapped bishop (like in the first diagram) was worth 3 pawns.