Investment fees have dropped so low that you may have assumed they have gone as far as they can, and the cost-cutting story is just about over.

Well, think again. Something mind-boggling is on its way.

Fees are on the verge of falling below zero. Major companies will soon be paying customers to invest with them. That, at least is the conclusion of the investment research firm Flowspring, which says the fund price wars are about to be fought in the previously unexplored territory of negative fees.

“Zero may seem to be the lower bound for fees, but it’s not,” Warren Miller, Flowspring’s chief executive, said in an interview. “As we’ve learned from interest rates, zero is a psychological barrier, not a real one. The fund industry is tottering on that barrier right now. Negative fees are coming.”

In a provocative essay, “The Game Theory of Fund Price Wars,” Mr. Miller writes that competitive fee-cutting has brought us to the edge of a new, negative-fee universe that is probably better for individual investors than it is for investment companies.