When Facebook groups loses their administrators/moderators, the group will also suggest a new promotion for the group. Either you could choose yourself, or someone that you think could be “the perfect administrator”.
This is normally done with a notice in the right column on the screen (unless you’re not in the new design). By means, promote a new administrator can only be done if the entire group are missing a “team”. Tornevall Networks built a plugin that automates this promotion when a group is entered via Chrome.
It also, partially, can do this via Facebook group bookmarks. That part of the plugin isn’t perfect as it could crash if your group list is too large. Not due to the large list, as it opens one group at a time. This is still under bugchecking. However, the plugin has best effect on often-visited groups. You can find it in the link below.
Currently, there is a work in progress with the new Facebook design. We will come back to that later. And by the way, the plugin is “multilingual supported”. Groups can be promoted regardless of which language you’ve chosen and in a few different ways. As you might not want to promote yourself as an administrator in racist-groups, there’s a switch that allows you to accept before promotion.