What is the cancellation policy for United when there is a medical reason precluding the flight?

You and any persons on your itinerary will be able to reuse your tickets if they are wholly unused, to any where and any time you wish to travel. Most tickets unless unrestricted (read very expensive} will have a change penalty of at least $150 per person. With proper documentation (doctors note or hospital bill) will allow you to request a refund of the change fee less a $50pp processing fee.

You will not be able to get a full refund, but you can you can pay the change fee of at least $150 pp and get back all but $50. You will have one year from date of purchase to pay this penalty and reissue your ticket and you can fly after the one year if you make the change for beyond the expiry but pay before that time.

I am sorry to say that:
The only way to refund your ticket is if the passenger dies. If this is the case, you will just need to submit a death certificate.

Allyson, please let me know if I can answer any further questions about this matter.