Name change because it's a very delicate matter.
Yesterday I met with a friend and our parents (her DF and my DM) will end up in the same circumstances. If we don't move them here with us they'll end up dying alone.
Neither of us have family left in their home countries, and the current visa situation means that we'll never be able to bring them here (legally). Sit our plan is to bring them to live with us for the last couple of years of their lives, and take them to private doctors so they don't get deported. I believe that's the only option.