Girlfriend lost job, can't make her car payment l. Should i buy it?

My girlfriend got a 2017 Toyota Corolla and has only $4000 left on it. She has a savings account with $70,000 in it but absolutely refuses to touch it because she says shes leaving it for her kids. I tried convincing her to use it to wipe out the car payment and just refill it later, but she refuses. She offered me to buy her car for the price of the debt. Im conflicted on this because our relationship has been rocky. If i buy it and break up what happens? The car would be in my name. $4000 is a steal for a 2017 Toyota Corolla but id really like to continue saving my money to pay off my mortgage.