It sounds like you live in the U.S. What a nightmare this place is.
I'm not suggesting there's anything ok about being forced to choose between domestic abuse and homelessness. There's not. That's totally fucked up. I'm just putting this out there because it might aid in decision-making.
I do know women who have spent time homeless and come out the other side. Referencing women because that's what you appear to be, and because the risks are different for female homeless people. Obviously, what you really want to be able to avoid is ending up with yet another abusive "protector" who will force you into sex work or carrying their drugs around.
The women I know who are still on their feet a few years after a period of homelessness pretty much all either connected with social service programs of one type or another, or else they met someone who gave them somewhere to stay and the means to sort things out. These women all have above-average people and communication skills, which helped them make use of opportunities when they presented themselves. Formal education is helpful, but they didn't all have it. However, they were (and are) people who could walk up to a stranger and ask, "How do I survive here? How does this place work? What's the first thing I need to know? What's the second thing?" (Probably not those literal words, obv.) They're also all people who are comfortable setting boundaries. They'll tell you unequivocally what is and isn't ok with them. They can negotiate and think on their feet.
I considered leaving home for the streets as a teenager, but I possessed none of the above qualities, and wouldn't have made it 2 nights. I was timid and trusting and obedient, so you can imagine how that would have gone. I probably have the skill set now, but no longer the basic physical resilience. Homelessness isn't a realistic option for me, so if I were ever forced back into an abusive domestic situation, it would be ctb time for sure. Others might be able to make it through a homeless period and come out ok, though.
Also: One other thing that's immensely useful if you're homeless is to have a car to live in. Cops routinely break up tent cities and throw away the belongings of everybody in them. Sometimes shelters are viable options and sometimes they're not. A car keeps you out of the weather and lets you move on in the event of police harassment.