There are small, private nonprofits all over the country offering services like food pantries and other household items. It might be worth looking into just as a plan B in case their benefits run out (most likely at some point.)
For health care, you can look into purchasing a plan for them via the marketplace + tax credits. The tax credits don't count as a means tested benefit so there's no issue with immigration. Generally speaking healthcare for elderly parents can be an issue due to expense, just something to think about and budget for if they can't get Medicare or SSI anymore. There are some lost cost or "pay based on your income" (aka "sliding scale fees") clinics around if you search for them, but if you're looking for regular, ongoing health care then some kind of insurance will be needed.