The complete refund and free return to destination is called the "trip in vain" policy of some airlines. It puts you on the next available flight to your origin according to the ticket (and you don't get any FF credit at all). It's not part of EC261 and no, you cannot return to your origin six months later.

If you miss your connection, EC261 requires that you be rebooked to your destination by your airline at no additional charge; normally you should NOT buy a new ticket yourself. EC261 also provides for duty of care (meals and lodging) if there's a long delay for just about any reason.

BTW, the term connection requires that your flights be all on a single ticket/PNR.