That's true to an extent, but equally there's simply no support for the many women (and men) who also struggle with life skills and/or mental health issues or autism, and/or end up homeless, but don't commit crime - particularly not VAWG (or violence against other men).
Some may commit what could be described as survival crimes (theft, shoplifting, or self medicating with illegal drugs). However they don't rape or beat women up.
There's also many homeless people who don't have mental health issues and/or lack of a job. Many are or were in work - until homelessness made it too hard to hold the job down. They're homeless because private rentals are expensive and there's not enough social housing.
As I said before, many sexual predators and DV perpetrators don't change. That includes many who aren't, never were, and never will be homeless whether they've been in prison or not.
I know several women who've been the victims of these crimes.
In more than one case, the victim is the one who ends up homeless - whereas the perpetrator is doing just fine, living with parents, moved in with another partner (likely new victim), or simply back to the house he owned.
There might be a case for "survival crimes/crimes of despair" but there's no justification or excuse for sexual assault, rape, and DV.