39Hoffmann degradation requires a halogen molecule to be present....during Hoffmann degradation, some amount of base may add to the carbonyl group, but given the chance, it finds abstracting a proton from the amine group easier. The double bonded amine group then attacks the halogen-halogen bond as a nucleophile.
The part upto which the proton is abstracted is an equilibrium reaction. The proton may be given back also. What drives the reaction after that is the nucleophilicity of the double bonded amine (-NH) group. After it attacks the halogen bond, the reaction cannot "go back". It must proceed.
