There is no claim system in the game, so it wouldn't work out all too well. Even if you wanted to solo it, someone else could come by and think you'd like help and engage, at which point you'd have to both fight it and have an angry discussion about "Go away, I'm soloing".

And this is if they had no loot. If they had loot, you'd just see everyone zerg it because the zergiest person gets the loot.