My mom bought and signed a contract for an insurance policy. Can she break the contract and if so how?

It sounds as if your Mom may have purchased an annuity contract. One form of this is to give the insurance company a lump sum of money and they provide a stream of payments back to you (including earnings) often for the rest of your life. Without more details, it's virtually impossible to offer more guidance. You can call the insurance company directly and get details of exactly what was purchased. The payments she receives can help pay for the nursing home charges.

Well if she is in a nursing home, how did this happen? If this was recent, call and cancel it. Usually they will cooperate with you. If they are already paying out, it may be an old policy and you are bound to it's terms.