To be honest, it may not be clear at the time if we're actually helping someone or if they're just taking advantage of us. Not everyone wants to change; some people only want to stay the way they are.
But what is clear is that they have a need, and God has put them across our path to do what we can to help them. Jesus once healed 10 lepers but only one came back to thank Him; the others were simply taking advantage of Him (see Luke 17:11-18). But did that mean Jesus shouldn't have bothered with them? No, of course not; one man was changed, both in body and in soul.
At the same time, your cousin is on a dead-end road, and simply providing her with food and shelter isn't solving her problem. She needs help, and you are in the best position to get her to it; she won't find it on her own. Ask your pastor, doctor, or other knowledgeable person what resources are available in your community to help her -- and then give her a deadline to get connected to them. You've probably heard the expression "tough love," and the time has come for you to practice it -- both for her sake and yours.
Most of all, pray for her, and ask God to help you point her to Christ. The Bible's words are true: "God is our refuge and strength, an ever-present help in trouble" (Psalm 46:1).