Can you die from a cat allergy?

Highly unusual: but one can never say never in medicine. The scenario I can think of is when one has severe asthma and is allergic to cat. In which case, the cat exposure can lead to a severe exacerbation resulting in death. However I have not seen a person dying from cat allergy per se.

Technically, yes: Some people are very allergic to cats. Some have "cat asthma" with surprisingly low exposure. If exposure continues and asthma does not get treated, asthma can cause death. One usually gets plenty of warning ahead of time, UNLESS one already is really in bad shape beforehand; asthma triggers combine "like water behind a dam". If not controlled (neglected or not recognized) fatal asthma can happen.

Yes possible: If someone has severe allergy to cat , cat exposure can cause people to die.