My brother and I recently made plans to visit our grandfather who was diagnosed with Stage IV lung cancer. We bought tickets for travel 4 weeks out and then he died 1 week after the diagnosis.
United was excellent about cancelling/refunding my brother's ticket and waived the change fee on mine so I could go to the funeral (which happened 5 days after he passed away).
The whole process was simple via a telephone call. It was really nice that United didn't make either of us jump through hoops.