In Pennsylvania at least, that is handled by the filing of a provisional ballot followed by a court system. One challenge to that solution is that there are hard limits on how long it can take for the election to resolve, so it is possible for that window to close before an investigation on an allegation of voter fraud to complete, and if it cannot be proven that that provisional ballot should be counted, the ballot is discarded.

The recourse should a person's vote be stolen that way is proof that the vote was stolen followed by punishment for the thief, and that punishment can be fairly severe because vote tampering cannot be taken lightly given the impact it can have on the process itself.