Here is what you can do, but you have to be fast about doing it, and get it done before the waiver period is up. First of all, check and see if the idiot that dropped all his players has commissioner control turned to on. If he does, you can use the commissioner tools to override the waiver priority system, put all the players back on his roster and then lock his team.
If he doesn't have commish control turned on, basically you do have to have some kind of draft to fairly allocate the dropped players. The fairest way would be to either give the last place team the first pick and go up the standings or to to give the team that had the last pick in the draft the first pick. At any rate, what you need to do is get everyone to turn on commissioner control on their teams when you decide who gets what player and then ask them who they want to drop for the player they want to get. Then, with the commissioner tools, you can override the waiver system and put the players on everyone's rosters, dropping the players they want dropped.
However, you have to do this before the 3 day or whatever waiver priority period expires or the waiver claims will just go through.