The struts/pistons are no longer strong enough to hold the boot (trunk for americans) open. I went to buy one from the shop only to find the price was for an idividual unit. Is there ever a case where only one would need to be replaced? - how can I test which one needs replacing if this is the case?
Sure: rust will kill anything but it does tend to start at a point of entry and spread. It could kill one strut before it dissolves the rest of the car. Likewise, a side or corner impact could bend a single strut.
Realistically, if you have a car of some years, I'd assume that they're both gone rather than trying to puzzle out how to squeeze a few more years / months out of one old one.
In terms of testing, you can pretty easily slap together a test rig with scrap lumber.
If you purchase a replacement strut and repeat the process, I think you'll find that you really want two news rather than one new, one oldish.
It has been my experience that the gas struts are similar to headlights. Occasionally one will fail early, but most of the time the second unit fails shortly after the first. If only one side is replaced it will take the load of the weaker side. This causes it to wear prematurely as it is carrying more than half the load. Also remember that any extra weight on the trunk/boot such as snow, bicycle rack or aftermarket spoiler will increase wear and shorten the cylinders life.