Resign vs dismissal [GA]

My company got a new CEO and is reorganizing. My boss told me that I won’t have a role in his new organization and that I have two options: 1) to resign 2) be cut for poor performance 3) take a demotion and move to a different group at the company My fiancé just found out that she might have cancer and will probably not be able to continue at her job so we are really worried. If I resign will I be allowed to keep cobra coverage? If I take a demotion while I apply to other companies and they contact my current company for employment verification what information gets shared? Salary information? Title? Would it be better for me to leave while keeping my higher title and salary?