I have a close friend that ran away. He was 16 and his mom called the cops on him but they told her that they can't do anything about it. Why didn't they?

Any number of reasons.
Have you ASKED the police why, would be the best place to start..

My state has specific statutes on teen runaways (not missing under suspicious circumstances) and the police don't have to try to find 16 year olds.