The parent only receives social security and has no other assests.
No, not just because they are your parents. You could be liable only if you agreed to be liable.
You must agree to be bound in one form or another, or have a court order that you take responsibility for your parents. The law does not automatically impose liability for a parent upon a child. It can work in reverse and can also work between spouses under the doctrine of necessities.
This response is anecdotal in nature and intended only as a general background on the particular matter. I DO NOT REPRESENT YOU. For legal advice on your particular situation, you must contact and retain counsel. If you would like to retain me, representation will be effective only upon the execution of a signed retainer agreement and payment of appropriate fees.