For how long can a contract stay alive?

Gas is burned when a contract is executed. That’s fine.

How about a contract that never runs? Can the (state of a) contract stay in memory forever or will it be dropped at some point? If forever, is this a potential concern?

I was under the impression it would be loaded in RAM only when/if it’s executed. If it doesn’t get executed, then it just lives in the blockchain like old transactions.

Does it say somewhere that contracts stay in RAM?