But sometimes, they don't stay because they're not allowed to keep their pets with them.
That was the rule at a shelter in Kansas City, until one victim and her heroic dog needed help.
The rules have now changed. And so has the shelter.
CBS News referred to her as Mackenzie, and kept her face out of focus on "CBS This Morning" to protect her identity. Her life could depend on it.
"When your life is being threatened and you're in that situation, you don't think," she told an audience. " (You only want to) make it through the next blow. Make it through the next second. Make it through the next minute."
Her life has already been saved once - by her 140 pound Great Dane, named J. Matthew, who protected her from a brutal attack at the hands of her boyfriend.
"He grabbed me by my shirt and put me through the wall," Mackenzie told CBS News. "Literally (through the wall) -- dry wall, boards, nails -- to the other side."
Hearing the commotion, the dog came to investigate.
"And my boyfriend goes in to hit me," Mackenzie continued, "and J. Matthew lays on top of me."
He absorbed the blows meant for Mackenzie. Frustrated, her attacker picked up the heroic canine and threw him off the porch, then led him to a busy intersection. And left him.
Mackenzie escaped and rushed to a police station. Cops sent her to a nearby women's shelter - the Rose Brooks Center.
But Mackenzie was thinking of J. Matthew.
"I said, 'Let me go back and get my dog and I'll come back,"' Mackenzie recalled. "And they said, 'We really don't accept dogs.' And I just said, 'Oh, I'll drive out of town ... and we'll just stay at a rest stop."
Mackenzie says J. Matthew is so special to her that she weren't going to part with because of "the fact that he saved my life, the fact that he sacrificed his body for me. ... How could I not save him? How could I walk away from him?"
Mackenzie's not alone.
As many as 40 percent of battered women say they don't leave abusive situations because they're afraid to leave their pets behind.
Rose Brooks Center CEO Susan Miller told the same audience Mackenzie was addressing the center felt it had no choice but to make an exception for J. Matthew to its rule barring dogs "and I must say, I'm glad we did."
The center broke its own no-pets policy, and allowed Mackenzie to bring in J. Matthew.
"It was just great to see the bonding they had," Miller told CBS News, "the healing process they went through together. ... It really made us realize this was something we needed to do: We needed to provide this opportunity for women to bring their pets."
And so they did, unveiling last week a brand new pet kennel adjacent to the center.
It's dedicated to Mackenzie and J. Matthew.
Mackenzie says knowing her story helped create a place where pets are allowed is "awesome! It is amazing."
But the kennel is more than an accommodation to pets.
It is a potential life saver.
"To know that a woman will no longer have to make that choice, that they will either have to get safe or they will have to abandon their pet, is worth everything," Susan Miller says.
There is, Mackenzie says, "absolutely" no doubt that the new pet policy will save lives. "This pet shelter is life," Mackenzie adds.
Mackenzie is out of the shelter after spending 90 days there.
Mackenzie's attacker spent 60 days on probation and is now free.
To see Michelle Miller's report, click on the video in the player above.