Starting sometime around the late 1970s, the Mexican Peso started experiencing extreme inflation. By the late '80s, the price of a loaf of bread was thousands of pesos. The Mexican government introduced the "new peso" whose value was equal to exactly 1000 "old" pesos. In other words, they simply created a 1000-peso coin, but they called it a "new peso" instead of a "1000-peso" coin.

Bitcoin might one day have the same problem, except in reverse (because Bitcoin is deflationary), but the solution is similar. Introduce a unit that's smaller than a single satoshi (maybe you could call it a dannyhamilton?). It would require a bunch of software changes, but it's entire feasible, and it's entirely fair.