The question is not that clear and hence, we have conflicting answers.
If a GC Holder worked for 10 years and is over 65 yrs, he/she can avail insurance thru Medicare. If they are economically poor, they may avail a certain part of Medicare thru Medicaid.
If the GC holder has never worked here and is over 65, they qualify for Medicaid in some states like NY if they could prove that they have no income or financial assets. NJ, PA, VA etc wouldn't offer Medicaid to GC Holders who have never worked here.
However, if one is a citizen, never worked here and have no income, they qualify for Medicaid in most states.
Hope this helps.
ps: This is first-hand knowledge