That isn't a third category, those are people who have been convicted of a crime and want to commit another one. It's the same general category of not being able to solve people committing crimes by making already-illegal things even more illegal. And on top of that you get to add two new problems.

The first is the deterrent to reporting, both before and after a conviction. In the original case the victim now can't even report a domestic misdemeanor in the subculture where gun ownership is sacrosanct because either they themselves consider "permanently can't own a gun" too severe a penalty for the crime they were trying to report, or they know the perpetrator will and they're afraid of being booted out into the street or worse if they do it. And for someone who already has a conviction but still has a gun, now the other people in the household can't be calling the police for any reason because if the police find the gun the person keeping a roof over their head is going to prison for years. In general you want the penalties for things to be proportionate and making them disproportionate makes things worse instead of better.

The second is that the victim, or any future victims, are living in the same household as the perpetrator, and then how do you answer this question: Is the victim now prohibited from having a firearm? You're screwed either way, because if you say no you're denying the innocent victim's right to self-defense but if you say yes the perpetrator now has an excuse to have them in the house.

Then these things combine poorly because the overconfident drunk who wants a gun is willing to bet they can convince anyone it belongs to their sweetheart but the sweetheart is nowhere near as confident they can control what happens if they call the police.