If an elderly person has worked their entire life and been a contributing member of society, the government should step up and help them out if they need it later in life. Medicare is an example of this. The working elderly are deserving of this. Much more so than the mothers of 5 with 5 different fathers. We should give back to those that helped society throughout their lifetime.
If an elderly person has worked all their life (or raised children full time) but is somehow left without support, then yes, the government should help them. We owe these people for what they have done for the society. If they are old now, it does not mean they are no longer valuable human beings.