If he is not on the lease, does your lease permit you to have long term guests?
why is that? At best he is a lodger (my error previously using the term boarder). At worst he is a subtenant since he is not on the lease the OP has with the landlord.
Unless he admits to never providing ANY support for the household (i.e. never providing food, payment for a movie on cable, etc.) he is going to be considered a tenant as far as the police are concerned. The police are not going to run the risk of violating someone's civil rights and tossing them out on their ear without CLEAR proof they are not a tenant. The police will almost always "punt" and tell the occupant that the matter is a civil one and they will need to evict them.
Further, a "landlord" is the one that may evict, not another tenant. If the OP's lease allows her to sublet, then maybe she can evict him herself. But, if not, the way she will have to do it will be to have the landlord evict HER and her guest, and then (if the landlord chooses) allow her to return as a tenant.
If a lodger, he is allowed the same amount one rental periods notice. I do not know what the agreement was between the OP and her bf but I suspect it was the guy pays something each month. That would mean that he is entitle to one month's notice after which he is considered a trespasser.
The police will generally not make that call. They will almost always err on the side of caution. if a court believes him to be a lodger, then the court can order him out. The police are not going to enter that realm absent clear proof.
Unless he is sleeping on the couch and living out of a suitcase, they are going to consider him a tenant to be evicted.
I'll defer to your experience regarding the lack of action if he is a lodger but I see no reason the OP could not terminate the boyfriend's tenancy and seek an eviction should he not leave willingly.
Nothing prevents her from bluffing. But, if he calls her bluff, the police won't be there to force him out and she will have lost at least 30 days that she could have used towards the time for the eviction process.
what? Your courts do not impose an automatic restraining order in the case of domestic violence?
Nope. They can, and often do, but if the offense is relatively minor or the victim waffles or backpedals (and they most often do) the order will tend to be a so-called "peaceful contact" order. In some courts these are nearly automatic in felony cases, but not always so in misdemeanor offense cases. After an arrest the police can request from the court an Emergency Protective order with a move-out order, but that's good for no more than one week and the OP would have to then obtain a TRO or he could then return.
However, DV can allow the tenant out of a lease agreement under state law. But, the OP mentioned verbal abuse not physical abuse. At this point I suspect that an arrest or even a TRO are unlikely possibilities unless the verbal harassment includes threats of harm.