I would not have an emergency that the therapist would be a part of. I cannot conceive of such a thing for me.
If the therapist had an emergency with another client - and I guess cancelled or was late for my appointment - I could deal with it. I would expect a call to prevent me from showing up or an apology if a call was not possible. Other than canceling the appointment I had, I am not sure how an emergency with another client would possibly have anything to do with me.