I would contact an attorney to find out what your legal rights are if your parent doesn't have a will that states if they become unable to handle their own affairs their power of attorney can deal with their personal affairs.
If your parent is unable to sign legal documents, a child just can't take it upon themselves to sign things for them unless it is in writing in a will.
Contact an attorney because a nursing home can cost between 3,500-10,000 a month an the home would be sold to pay those costs if the state has to pay for the cost.
