Yes it is possible for a nursing home to take a persons social security money if they require it.
There's no law though that says how the social security money has to be sent to them whether the nursing home gets the social security money paid directly to them or a family member gets the social security check and then has to send it to the nursing home or if they have to pay the nursing home themselves out of that check.
With my grandma who had social security and went into a nursing home they took her social security check within a few months of her being admitted to the nursing home.
If someone has no money and needs nursing home care and cannot pay for the nursing home care out of pocket then Medicaid will pay for the nursing home care.
If you have no money then the patient needs to get signed up for and hopefully approved for Medicaid which will help pay for a patients nursing home care when they require it.
Paying for a nursing home can be expensive and some people have to sell their assets such as home, cars etc to help pay for long term nursing home care.
So make sure you get some type of health insurance such as Medicaid which will help pay for the nursing home care.
Also a nursing home can refuse to take a patient back especially if the nursing home patient is being a threat to the nursing home staff or to any other patient in the nursing home.
Some nursing homes that are not equipped to handle combative and violent patients may decide to discharge that patient from the nursing home and have the family or someone come get the patient.
The nursing home cannot just dump the nursing home patient out on the street but the nursing home staff can discharge the patient and refuse to allow them to stay there.
That is especially true if the nursing home is privately owned.
It's up to the nursing home as to whether or not they want to care for that patient.
If the nursing home refuses to take in a patient or take the patient back then all you can do is look for another nursing home that will take in the patient.