I know that the concept of negative reputation doesn't theoretically exist, but in practice, if you look hard enough, you can find users that have negative reputation; it's easier to see this in the reputation graph.
There are a few examples of users with negative rep (one user on meta has -700 rep). The whole purpose of rep is to determine how much the community trusts and values your opinion, but also what rights you gain from it (voting, commenting, editing etc.). Having users with such a low score certainly must have consequences.
Shouldn't there be some sort of action taken for this low, low, low reputation? We can't take any more rights from such users because they're already only allowed to ask questions (at a slower rate than most) and answer questions (also at a slower rate). Taking these rights away will strip away the possibility of ever gaining rep back. However, a short visit in the sin bin might be a better solution.
We've already seen the sin bin used, on various occasions, for different types of infractions: abusive behavior, spamming, offensive names/avatars, gaming the system etc. Having a penalty for low rep that's automatically enforced would make the binning process somewhat more transparent and would deter users from continually trolling the site with no consequences (they clearly don't care about rep, so just downvoting them won't have any effect).