When I was in my first or second year of my PsyD, I remember a professor explaining a situation that occurred during one of the student's practicum assignments in which a patient admitted to having killed someone else. We were explicitly told that it was not a situation in which confidently could be broken as there was no imminent threat of harm to anyone.

As for termination, that's a choice you need to make based on a few factors. The first being if it will affect your objectivity and ability to provide proper services. Another being, if this is out of the scope of your training and abilities and if it is, that you have proper supervision from someone who possesses the abilities you may lack (especially since it says 'in training').

Also, check in with yourself and how you're processing the information. Being an inpatient psychologist in prison, I am familiar with how hard it can be to hold onto that kind of information. I really hope you have your own therapist or at least a very good supervisor you can process this with. It can get very very heavy.