Is there anything in the bible that supports Christian women staying with abusive husbands?
There is nothing in the Bible that requires a Christian wife to live with an abusive husband. There is nothing that specifically allows her to leave the husband either.
In my opinion, for what that is worth, this falls under the principle that saving a life may take precedence over God's commands in some cases. Jesus endorsed that principle in Matthew 12:3-4. "Have ye not read what David did, when he was hungry, and they that were with him; how he entered into the house of God, and did eat the showbread, which was not lawful for him to eat, neither for them which were with him, but only for the priests?"
It may be necessary for a woman to get a civil divorce in order to leave an abusive situation. Because of what the rest of the scriptures say about divorce, however, I would recommend that she not marry, at least until and unless he were to die.