I saw a really bad answer to a question on StackOverflow the other day with many downvotes. I've just been wondering if there is a defined limit to how low a question's score can go.
The lowest score a post can get is equal to the number of users who have at least 100 reputation, minus 1 if the question was asked by one such user. That is, if everyone who could went and downvoted the item.
Note that the actual lowest score on the site can be less than this amount. Downvotes aren't retracted if a user ends up below the threshold, so the actual possible lowest score is equal to the largest number of users to simultaneously exist (not consistent with the number of users in total, due to account merging and deletion). The above number would be the more reasonable and practical one, this would be your "theoretical lowest".
It's unfeasible for such a question to survive long enough without actually getting deleted (it would have to be a monster to get THAT low), but that's not automatic. If it does survive for that without intervention, it's rather unreasonable to arbitrarily limit how many people can cast an opinion on a post. The same would qualify for how high a post can go.
I guess the absolute minimum is -2,147,483,648 (i.e. no limit).
As of today there are 37,086 users having rep ≥100 on SO so the minimum would be -37,086 today.
The lowest scored question still not deleted is Create A Compiler For Windows standing at -76.
The lowest scored answer still not deleted should be this answer at -48.
(see also What are the most upvoted/downvoted questions and answers on the sites?.)
I don't think any non-community-wiki questions/answers will survive below -100.