My mother is a NJ resident who had a stroke that has left her partially paralyzed and unable to perform several activities of daily living.

You will not ever be financially responsible for your mother. You may have to sell her home in order for her to qualify for Medicaid benefits.  She will need to have only $2000 in assets, and other financial requirements such as no life insurance that can be cashed in, no real property, and other things.  If she requires this level of care, she should be in a facility where the care can be provided, and she will have to seel the house to pay for that care.  While the house is on the market, she will be eligible for Medicaid benefits.