In reply to Jamie Bankhead:
Traditionally, the broad consensus seems to be that gear which has been abandoned is fair game, but gear which has clearly been lost should be returned, if possible. If someone accidentally leaves a friend at the foot of a crag while packing up, that's obviously been lost, but if it's left stuck in a climb and someone is subsequently able to remove it, that's crag swag. Likewise, if you have to leave stuff behind when baling out, that's crag swag.
The distinction to my mind is whether the gear has simply been lost or deliberately abandoned. If stuck cam can later be removed, that means the original owner didn't try hard enough to get it out. If gear has to be abandoned during an epic, it's still the choice of the climber to leave it behind - it may be choice that's forced on them by circumstances, but it's still a deliberate choice, compared with forgetting to pick up something at the end of the day. Harsh but fair!
I am referring here to climbing ethics rather than the legal situation. However, so far as I can tell (I am not a lawyer) the law broadly supports the notion that a finder of abandoned property can claim full ownership even against the original owner; however it appears the law is not entirely clear and this is not an absolute rule.
Of course, individual climbers have different attitudes - some take the old-school view that everything is fair game, while other will try to return everything. I think most people would regard it as pretty low behaviour to take gear which has been temporarily unattended in order to help an injured climber, but it happens.
The example quoted seems to me to be a clear example of abandoned gear. From what I've read on the other post, they set off too late (for what is a popular, and usually busy, route), and weren't adequately prepared or equipped for that type of climb (no abseil devices, for example). They made the decision to cut the rope (they may have felt it was their only option, but nevertheless they made that choice) and they decided not to go back the following day to try to retrieve the stuck ropes. Definitely crag swag.
The value shouldn't really have a bearing. If you've abandoned gear then you shouldn't expect to see it again, although if it's something expensive you'll obviously hope the finder will be sympathetic. Likewise, if you find an abandoned rope or cam you might be more inclined to return it than a single nut. But this is a question of conscience rather than principle.