This would (at least in part) mirror the dynamic during another major period of collapse and upheaval - the migration period. Displaced people trying to survive by raiding or squatting on new territory, thus displacing more people and collapsing complex networks of trade which were sustaining large local populations, thus displacing more people etc etc.

Similarly to the end of the bronze age, it was also a period in which shifts in climate stressed social structures. A runaway dynamic of lots of desperate people on the move is not great for stability, and if everyone is already experiencing some scarcity, then that's all the more vulnerable.