Essentially, your personal status and power and how you can marshall that to protect yourself – how many people know you and would put up a fight if someone grabbed you or might recognize you on the auction block, how many bodyguards and what kind of home security you could afford, what kind of neighorborhood you could afford, how much trouble a kidnapper would get into if they got caught, etc.
But there weren’t any guarantees – look at what happened to Plato when he was enslaved as punishment by the tyrant of Syracuse. If it hadn’t been for a friend who happened to visit the auction block that day who bought him and then manumitted him…