I had friends at a very popular fraternity at a major college (and later served on a discipline board). This fraternity had a series of violations. Mainly underage drinking, poor grades, and complaints from girls (nothing even close to rape). So just a series of dumbass fraternity guys acting like dumbass fraternity guys. Seriously what do you expect when putting 20-200 guys between 18-22 in the same housing.
For these smaller infractions the school will warn both the local charter and the fraternity national headquarters. Each school has its own rules. So I can't say that one violation at one school is handled the same as another. Also when I say a school has rules I am being very liberal. [A school will have an advisory/disciplinary committee that will basically do whatever it wants]
A school may have outlined several examples of violations (hazing, drinking, grades...) and then their punishment for those. But I have first hand seen how hazing has turned into - boys will be boys - because someone on the committee went to school with one of the boy's fathers. Or another dad makes a big contribution right after he got in trouble.
So a school may do pretty much whatever it wants from putting a fraternity/sorority on probation, from expelling members of that fraternity, from taking the charter away from the fraternity. And it doesn't matter if the house is off campus or not. In the case I mentioned above, the fraternity owned a house about a half mile off campus. The university read the boys the riot act, said they were closed, or they could leave the school.
I have first hand seen both good and bad things happen using the school system as reinforcement.
- School can act much faster than our court system
- School can make people "testify" (based on most honor codes)
- School usually has some reasonably smart people making decisions
- It is easy to cover things up. I had a friend get assaulted on campus. The campus police did next to nothing and it didn't get reported as an assault to the actual police because the university was worried about their crime stats. Friend found out nothing was happening, so reported to the police... case was too cold by then to get much traction.
- One influential person can taint any committee. Several times I was told to vote a certain way (or I wouldn't be on said committee in future). Let it be known after I refused once that 3 committee spots were cut including mine - and then 3 months later 5 committee spots were opened.
- Once things hit the press a school will do damage control not get to the bottom of what was actually happening. See the Duke lacrosse team as a perfect example.
Answer in short: The school will threaten to kick out any students that don't abide by their rules. So even if a "fraternity" isn't nationally chartered and doesn't have any direct correlation with the school the school can still have said fraternity disbanded or the members face expulsion. This threat happens all the time but is hardly ever enacted on. The students really have no discourse except for talking to the press (which in some schools can lead to expulsion).