No-thanks: What if a player has no card? | If a player hoards cards?
First off, did you remember to randomly remove 9 cards from the deck? This would greatly reduce the chance of a player getting lucky enough for that to be a good idea.

Other than that, it is certainly possible that a player could get negative points (though I don't think I've seen it happen). If you have a player that is purposefully losing the game by just taking every card, and thus making the game unplayable for the other players, then it is simply an issue of sportsmanship, and not one of rules. The rules do not prevent a player from ruining the game in this way.