It is a tricky question. We have had to deal with last minute changes on our flight plans due to a death in the family a few times over the years and in both cases United was happy to step up and help us. That said, we were canceling plans to travel else where and had to postpone those plans. I would call an ask before spending money on trip insurance, I would also do what mahasamatman suggested and check to see what coverage your credit card offers. UA has been pretty good about changes for deaths but they will want a copy of the death certificate or an obituary to verify things.