Looking at the list of users, if one goes to the final page, one notices that there is people with negative reputation. Why they have negative reputation? Isn't "$1$" the minimum a user could have of reputation?
One cannot have negative total reputation, but one can of course lose reputation during a set time period. Bounties are a popular method for such reputation losses. In the reputation leagues for a fixed time period (the last week/month/quarter/year), the reputation change during that period is listed. In the all-time reputation league, the current total reputation is listed, and that is never below 1.