What about those on the periphery, with minimal protection from the state both before and after the fall? For them, the only real difference was the tax collector stopped showing up.

Tax collector never stopped showing up - tax collector was just working for someone different after the Empire fell.

As for those on the periphery, the only ones which would have fit the idea of those with minimal protection from the state would have been those literally outside of the borders of the Empire - the Early Empire pursued highly proactive anti-raiding strategies on the border, with large forces ready to respond to any incursion, while the Late Empire stationed many small garrisons along all the borders.

Furthermore, there is ample evidence that the benefits of the Empire reached into the periphery, including the benefits of long-distance trade, high-quality consumer goods for the working class and peasantry, architectural expertise, and resolution of legal disputes.

Please don’t take this as analogous to the modern day in any way. A modern village/town will break down rapidly without access to modern logistics, which was not the case then.

No, places broke down then as well. After the Roman presence in Britain left, Britain itself not exactly being in the heartland of the Empire, the resulting collapse into infighting and outside raiders was so total that even things as simple and universally needed as pottery suffered a horrific decline in both amount produced and used in domestic consumption and in the quality of the work, to the point where post-Roman British pottery is instantly identifiable compared to Roman British pottery. Some 200 years pass before pottery quality begins to recover. Aqueducts stop working in short order if not dissembled and cleaned, lower quality roads (via glareata and via terrena) fade without regular maintenance, brigands destroy all semblance of trade and free travel, even farming techniques decline with large-scale local mortality without the ability of skilled migrants to transfer location and then transfer their skills.

Civilization is fragile, in all cases.