An unprincipled person follows no moral code, has no integrity, and should not be trusted, like the guy who offers to help an old lady across the street but steals her purse instead.
No, unprincipled isn't a word we use to describe a school that's missing its principal — we're talking about the -ple word here. If you don't have principles, which is what unprincipled really means, then you don't have scruples or morals. You're likely to do just about anything bad, like break rules, take advantage of people, tell lots of lies, and extort people's lunch money.
adj lacking principles or moral scruples
without scruples or principles