In one of the episodes of Dan Carlin's Hardcore History, he asks the listener to imagine living in, say, England in the waning years of the Empire, and suddenly receiving a letter informing you that the Empire needed their legions back, that they would no longer be supporting your roads, etc. etc. Did this really happen so quickly and suddenly? If so, how did local populations react?
EDIT: And to clarify, I mean the original, fell-in-395-CE empire, not later Western Roman Empire or Byzantium.
So according to Gildas, and later Bede, when dealing with England, the Roman military presence was withdrawn and the civil authority mostly tried its best to stem the gap with varying degrees of success, and things becoming more of a steady decline than a sudden collapse.
The Romano-British, for example, manage to succesfully raise their own armies which have some success in defending against raiders, but without the Imperial logistical capacity to replenish ranks and equipment, and the economy to afford it, these are eventually whittled down, and the British become increasingly reliant on Anglo-Saxon mercenaries, who then take advantage of this.
People don't instantly abandon cities, but bit by bit, maintenance stops being done, people start moving to the countryside to farm rather than remain dependant on increasingly irregular deliveries, Roman buildings in disrepair are pulled down to provide stone work for more simple buildings that require less infrastructure to build and less upkeep.