Options are illiquid much like a nanocap equity.
There can be long stretches of time before such securities are traded, but all during that time, market-making algorithms are there with bids and asks waiting to be filled.
The difference between an option and an illiquid equity is that the price of the option derives mostly from the underlying equity, so if no option trades have taken place, yet the underlying has moved considerably, the option limits generally follow, with a strangely deviant last price.
Limits for illiquid equities don't tend to move much without a trade because without new information, the cost to hold a position is mostly the interest rate.