A fallen empire setting would be a perfect environment for adventuring - a lot of ruins (or abandoned places) to explore and little authority to drive back the monsters and bandits except for the PCs. Not to mention the treasures the empire has left behind when retreating in a hurry...
A collapsing empire would create a power vacuum, and many opportunists will try to fill it - thugs, monsters, would-be kings, tyrants, even a few heroes. PCs could become kings by deposing a despot or defending villages against the monstrous hordes when no one else would.