I can understand your concerns about this. I worry about my T being ill or dying but she is in private practice from her home so I would find out sooner or later. I have never asked her what would happen but have always assumed that since she works in this field and clients are vulnerable etc. that she would have something in place that someone would be able to access in case of her absence to let her clients know. I may actually have to ask her...

I do find your therapist's reply a bit odd...to say that it wouldn't be possible to let you know? Surely she must need to have some backup or someone to inform those she is working with if she is no longer able to.

I hope she comes back to you with something more concrete.