OP, interesting question, which probably doesn't get addressed as much as it should in our education.
I would agree with the above poster that it is good to be compassionate towards the patient/family. And since each person deals with these issues individually, you could try to assess what that patient's needs are by saying "do you have concerns about the future"? They will let you know whether they want to talk further about it, and you can assess if you are the right "couselor" or if the patient would benefit from other mental health resources - clergy, counselor, psychiatrist, etc.
For yourself, again, you will have an individual response, and can seek out whatever resources would be helpful for you.
It's hard that in medicine, we often don't have the time/energy/resources to deal with these things in an ideal way.
But it's nice to think about these things once in a while. Kudos to you for doing so.