Every therapist has different policies regarding this situation but I would guess most would end the session at the "regular" time.

When something similar happened to me, my t did end the session at the regular time. The next time I saw her, we talked about how I felt hurt due to x, y & z. She listened and then said, "well, I have some extra time today, are you able to stay an additional 10 minutes?" ... so by asking for what we need sometimes, we can sometimes get results.