I've done a lot of reading about prison abolition, particularly academic sources, and the general idea is that crimes will still happen, but the communty will essentially sort it out on their own.
A lot of prison abolition frameworks rely on what we know about how societies met their own and each others needs before currency. So, if someone needed milk, they'd take eggs from their chicken and trade it with the person who has a cow. This ensured that everyone's physical needs were usually met.
Prison abolitonists won't say it, but their idea of how rape should be handled is exactly how these early agricultural societies handled it. It was a "majority rules" system. Meaning, if the community liked the women more, the man would be ousted or punished. And if the community liked the man more, the woman would be ousted or punished.
The general goal of prison abolition is not a society in which everyone is safe and has their individual needs met. It's a society that's stable and can maintain itself, where most people have their physical needs met enough to reproduce and continue the society.
This is why they can never give you a straight answer. Because the prison abolition framework doesn't aim to abolish rape, it aims to keep it as quiet as possible. Their solution is to keep men only raping their own wives and daughters, and for those women and girls to have enough other needs met that they'll shut up about it for fear of not having those other needs met.
Most prison abolitionists do not actually understand their framework, because they don't read the academic sources and they don't know how their ideal society would function. But the academics know exactly what it would look like, and it's a regressive society where instead of a justice system making prisons to keep the violent men contained, each household has a woman to keep that household's men contained.
If you want to know what prison abolition looks like, don't ask a prison abolitionist who says "I don't know what that would be like". Look at examples of early agricultural communities where their primary goal is survival. That's what it would look like, because in the absence of large scale people management, all of the social duties fall to women.