For Beyond All Reason, it seems the Spring/Recoil engine will eventually decide to "close the action window", so that if one player is lagging hard, they simply submitted no actions for that "round" and the rest of the players keep going.

I know because I've gotten to the point in the late game where my computer can't simulate at realtime, and I can no longer control my units, but everyone else keeps playing.

Conveniently you can even still sort of chat in this state, and ask a teammate to assume control of your army on your behalf.