Looking at one of the user's profiles, I observed that the user with current reputation 1 has the "Custodian" badge awarded for reviewing Suggested Edits. Now, https://math.stackexchange.com/review says that one needs "at least 2k reputation to review Suggested Edits". However, the history of this user's reputation shows that it never went above 2k during the lifetime of the account (actually, the user joined MSE this year and it was less than 100 at any time). How then this was possible? Was there a bug occasionally allowing users with any reputation to review suggested edits?
The description of the custodian badge says:
Completed at least one review task. This badge is awarded once per review type.
Whenever a suggested edit is made, the owner of the post receives the notification about the edit and he is asked to review it (even if he has reputation lower then 2k+) and his vote is binding, see: How do suggested edits work? and What happen if other users make edit on someone's answer?
In this way, user with any rep can get custodian badge for reviewing a suggested edit.
People with less than 2k reputation can still review First Posts and Late Answers I believe. (If I press "Review", those two aren't grayed out)
Also, as of this post I do not have 2k reputation and I have the Custodian badge as well.