One of my Virtual Families is a 59 year old couple who have not been successful in making a baby, nor have they aquired a child by a "soft knock at the door". What happens if they pass away without offspring?

Then you will lose.You need a at least 1 child so you can get the the next generation.Try and get an event.Good Luck

The game will be over. You can, if you wish, create a backup file (applicable if you are on Windows or Mac - not a handheld device) to see if you can get a child for the couple passes away.

You can find instructions on how to do this here. Note that the specific location of the savegame files vary between Mac & Windows.