The HSA is in your name. It is your account and goes with you if you leave employment with the university--including contributions made by the university. If you move to the Custom Network or PPO Plan, are on Medicare, or go to another employer that does not have a qualified high-deductible health plan, you can still use your HSA money for qualified medical expenses but will not be able to continue to make contributions.
Reviewed 2015-07-20