Are there airlines that will provide upgrades to Business or First at prices below full fare for those who need them due to a medical disability? I'm not asking about free upgrades, just any sort of program (advertised or unadvertised) to provide them at somewhat lower than usual cost.

(I'm thinking, along the lines of bereavement fares -- a fare for which you'd need to prove eligibility with a doctor's letter.) Does this exist at all?