Like Annasgirl says, your friend's idea is a bit confused, though I can see why she might have got that idea. Or it may be that she is just expressing it in a confused way.
There is a sense in which the Catholic Church says that when people marry, they become joined in a way that is not just a legal arrangement, it is more like an organic union. It sounds odd but you could think of it in the sense that when you marry, your spouse is not just a person you have a contract with, they are a part of your family just like your blood relations, and you are tied to them in a way that has a really permanent quality, even if you are estranged, it's not like dissolving a business partnership.
But your friend is wrong to think that the church would want her to stay in an abusive marriage. I think she's likely find that almost any priest who understood what was going on would help her work through leaving that kind of situation. Priests do want to see marriages heal where that is possible but most these days have pretty realistic assessments of when the situation is abusive and that is not a good option, and they will try to help someone in your friend's situation to see that. Practically that may just be separation or it may be legal divorce, both are allowed in those kinds of circumstances.
There is however a difficulty for Catholics, which is the teaching about what happens after that sort of divorce or separation. From the Catholic perspective, that organic union, though the legal part may no longer apply, cannot actually ever be totally undone, and so remarriage isn't allowed. That's a pretty hard thing to face for a lot of people and it may well be part of your friend's reluctance.
One possibility that can be looked into after a legal divorce, is the possibility of annulment (not legally, within the Catholic Church.) What this says is that the conditions for a valid marriage were not met in the first place, and so there was never that organic union. This doesn't look directly at what went on after the marriage happened, it looks at what happened before and at the time of the marriage. (Something that would clearly qualify would be someone who lied about their identity or was already married.) So an abusive marriage doesn't necessarily qualify for annulment. In practice however a lot of marriages like that, especially if the abuse was pretty much on-going from the beginning, do - essentially because the abusive spouse never intended to live according to his vows.
The annulment process takes some time and involves a sort of investigation. I've found a surprising number of people who get one feel that it is actually a positive experience, that it required a lot of reflection on the choices they made that resulted in marrying an abuser, and why they made them. But it's not a guarantee, sometimes an annulment isn't granted. (Possibly worth noting as well, if your friend is Catholic, and married in a secular setting or a non-Catholic church, without securing permission from her bishop, an annulment is fairly quick and easy to obtain.)
I hope some of this is helpful in giving you some insight. I think the most important element is that staying in an abusive marriage would be seen as not taking proper care of oneself, and that's no more allowed than divorce on a whim.