The athlete either would go home, or go lift weights, maybe mediball or tempo work, but the high intensity stuff is over for that day. It all depends on the athlete. Sooooo, the next workout doesn’t change (usually), just that specific workout.
If the PR was in the weight room, then I would finish the workout off, but discard the exercises that target the muscle group involved in the PR, more because of risk of injury than because of CNS fatigue. Of course in the weight room, PRs are always planned, and are never a delightful surprise, like they would be on the track.