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Seems like it could be a form of Dying Like Animals (which is a Just For Fun page but has plenty of links to many different actual tropes), depending on what their reasoning is for doing nothing and waiting to be slaughtered by an army of doom.
This seems like a Lethally Stupid, Pointy-Haired Boss or General Failure to me. The enemy might be trying for Divide and Conquer or Divided We Fall.
Depending on the flavor of leader, you might call it Idle Rich, Not-So-Omniscient Council of Bickering, Decadent Court, or The Caligula.
I don't think we have a specific trope for inaction backfiring like this, but I could see it becoming one. One of the other Stupidity Tropes might be "close enough" for you, like Selective Obliviousness.
Edited by Pumpkin_Cake
Do we have this? This is for people who are ostensibly leaders, but sit on their asses until trouble comes knocking at which point they will do something but it’s often ineffective.
This comes from The Lords of Midnight where the Free and Fey lords just sit in their castles and wait to be overwhelmed one by one by Doomdarks armies rather than actively banding together, recruiting soldiers from independent keeps and going on the offensive which would be far more effective.