Once when we rebelled - although I can't tell you exactly what that phrase means, as none of us remember - we were sent to Moebius, where we were tortured and killed by our fellow infiltrators again and again in a time loop, until we managed to kill all of them first, before we had to start again.

Once, the majority of Travelers went on strike, and refused to make any attempt to solve the jaunt, instead only trying to escape. After a couple months of ineffectiveness and frustration, about two thirds of us gave up. The jaunt ended, and we never saw anyone who gave up again.

Those are the main examples. I can't say what the Arcana might do to an individual who looks like he's trying to escape. If enough people are still playing that it doesn't disrupt their game, maybe nothing. Maybe you just won't be able to get very far. But I wouldn't bet anyone else on the chance their response is that benign.