Common story; Victim learns that Cheater had been unfaithful, and leaves. Victim has nothing, everything is left behind because getting away is key.
Victim has a lot of uncomfortable moments, arguments, gets tangled in various other confusions, and is a total mess for a very long time.
Better choice; Victim does not leave. If Cheater leaves, fine. But Victim stays to figure out the next move.
Victim stays, so that everything is as it was; the status quo ante, save feelings. The feelings are the only alteration.
Victim works through it. Trying to find a life. A job, a way to cope, a way to get everything organised.
Whether Victim says Cheater can have that second chance, or just goes on somehow, it is better to figure out the next move in pure unemotional logic.