Technically speaking, a cat can continue to be an expense either directly or transitively, possibly forever, as long as the cat is fertile, has a fertile mating partner in reproductive age, and recursively produces successive generations of descendants, each one consisting of at least one live-birth of fertile cats surviving to reproductive age that you agree to be economically responsible of.
This duration would have an upper bound equal the minimum between your own lifespan and the ownership period of the cat(s).
What's wrong with going to the shelter and getting an actual cat.