Unless it has been decided that you are legally responsible for the care home fees, you are not obligated to pay.
If the person meets NHS Continuing Healthcare Funding criteria, the NHS will be responsible for paying entire care fees, nursing care, social care and other costs related to their care needs.
You are not obligated or avoiding care home fees for your family members unless you hold joint assets or have signed a home care contract.
If your family member wants to get into a care home that is over their budget, you or a third party can volunteer to pay the fees. If you agree to pay the top-up fee and you sign a contract, you will then be under obligation to pay the pre-agreed amount.