Sprint Corp. has for years overestimated how many of the low-income Americans it provides wireless service to through a federal subsidy program actually use their phones, according to regulatory documents reviewed by The Wall Street Journal.

The No. 4 U.S. wireless carrier by subscribers is facing a potential settlement with the Federal Communications Commission after the regulator in September said Sprint improperly collected “tens of millions” of dollars in federal subsidies for 885,000 customers who weren’t using the service...