It depends on the school, and the school system. Some do suspend bullies, and expel habitual ones, especially some private schools (though some private schools are pretty sorry).
Some schools, some systems, will make a genuine effort to reform the bully and try to make them into a productive student, and citizen. Really, there are schools that do this, as hard as it may be for some to believe. Of course, there are schools that don't do it. Mainly because they're staffed by burned out, overworked, or just plain lazy people and administered by incompetents, or even active malcontents.
This is one of things -- one of many, many things -- that can't be talked about in absolutes. It comes down to the actions and intentions of individual parties.
Businesses have a profit motive. It costs money to train staff and keeping bullies around increases staff turnover, meaning you have to continually hire new workers from a vanishing pool as word gets out.