There is nothing wrong with asking the police about quitting. IMO I would reckon that most LEO would probably consider that particular assignment a rather crappy assignment. They are sworn in and have taken an oath similar to the military. If an order (unlikely) came down the chain to go into the hospice and rescue Terri most would be moving at lightning speed. I know I would anyway.
Listening to people they don't even know trying to get them to quit their job would make it so.