A-3TWENTY: Nobody says fire the controller ! This is your interpretation of my words "somebody has to go". This could be the ATC Boss of the airport, the one who makes the roaster or maybe the controller, when he has a responsibility for such bad work.
I assume that we talk about the approach and ground controller in one person. When you are familar with German ATC rules, you can read that in cases service cannot be continued, the regional ATC Center must be informed. This shoudl have been done as the minimum by anybody of the people involved, before leaving the tower and stay unstaffed.