What can happen if a benign brain tumor goes untreated?

Depends: It depends on what type of benign brain tumor it is and where exactly it is located. Some benign tumors can be watched, but some require treatment. Please write back with more details about tumor type and location.

Can be fatal: Benign brain tumors, because they grow inside the skull cavity which is full of brain and cerebrospinal fluid, will press on the brain or displace brain tissue when they get large enough, and this can cause seizures, neurological deficits, or tissue shifts ("herniations"), any of which may be fatal if ignored.