I can understand why you wouldn't want your daughter to have a friend over all the time. Your daughter needs to spend time with your family, do homework, and get into sports/hobbies. It would be reasonable to tell your daughter that she can only have friends over at X-X time and on X days of the week.
Is this what you mean because I can't imagine that it costs that much to have a kid over.
What I'm getting at is that kids don't abandon their own homes for no reason. There'll be a good reason why this kid is at your house and hot her own. I would do whatever you can to allow her to keep coming when she needs to.
Like I said, it's in the best interests of your daughter and your relationship with your daughter to draw boundaries. It's your job to make sure your daughter is doing her homework and that she has space to do activities. Talk to her to find out what's going on--whether she is OK with the current situation.
If she is, I would try to make things work. For example, you could have a rule that the girls go to opposite areas of the living room to do homework at X time of the day after school. This would benefit both of them. You could talk to them both about getting on to a sports team, running around at the park, or joining a community activity.
Many people are talking about "safeguarding" but I don't think you should pass responsibility for this situation on to the school or police. Yes, talk to them and make them aware of what's happening. Try to find out by talking to the girl what's going on in her life. But the bottom line is that YOU are the adult who is most involved and I genuinely think you should do your best for this kid. When you're 90 and looking back on your life, you'll want to feel like you made a positive impact on the world.
My parents were extremely violent and I hated going home because it was dangerous. I wish I had had a place like yours to go.