A relatively popular method of killing enemies in abyssea is gathering a lot of them, then defeat them all with area-of-effect weaponskills or magic. Unfortunately, this leaves many of the enemies in an unclaimed status, and anyone with ill intent can walk up and unleash their own aoe just before the original puller kills them.
It gets even worse.. if the original puller would do anything to prevent the 'theft' of the pulled enemies, be it prior to the 'theft' or after the fact, they are at risk of GM intervention for disruptive or malicious acts of griefing. This isn't just speculating either. People HAVE received account warnings for this from GMs fooled by bad faith GM calls.
There is a way to avoid this rude and offensive behaviour from even taking place: the 'ownership' of an unclaimed enemy lies with the first person to damage it in any way. So even if someone runs up to your gathering of near-death enemies and kills them with one Fell Cleave, Aeolian Edge, Meteor or otherwise, he'd only get credit for the mobs actually claimed by him, while any experience and items of remaining unclaimed defeated enemies would fall to the person or group that landed the first damage.
This still allows people to pick single mobs out of the swarm of enemies, but it would discourage the very disruptive and rude behaviour seen now, where one person claims the rewards while letting another do all the work.