stay longer than round trip return airline ticket?

You are incorrect, once the date has passed for your return your ticket is worthless. Ask for a fully flexible ticket where you are able to change the return date usually for a small fee if not free of charge. Also ask about the cost of a six month or year long ticket as with any ticket, you have to stipulate a return date, and having a year ticket you have ample choice to bring the return date forward.

If you haven't contacted the airline and made arrangements, when you don't show up for your flight, that return ticket is cancelled, do not pass go, do not collect $200. Or in your case, that return ticket isn't worth the paper its printed on. You won't be able to use to fly standby.

You will usually need to cancel your return reservation before the flight departs. Then you can usually use the return segment on another flight. Some airlines will let you use the dollar value for any of their flights, or you may only be able to use it for the same destination. You may have to pay a change fee and will usually have to use the credit within a year. Different airlines will have different policies so it would be best to contact your airline for specifics.

No, that's not right. Visa aside, if you make no arrangements ahead of time your return ticket simply becomes void when the flight leaves.