Many people who obtain health insurance through their employers—about half of the country—could be at risk of losing protections that limit out-of-pocket costs for catastrophic illnesses, due to a little-noticed provision of the House Republican health-care bill, health-policy experts say.

The provision, part of a last-minute amendment, lets states obtain waivers from certain Affordable Care Act insurance regulations. Insurers in states that obtain the waivers could be freed from a regulation mandating that they cover 10 particular...