There are no generalizations to be had and thus, it is important to post the specific situation in the specific board for the carrier in question.

1. Some carriers will cancel/change tickets upon proof of the death of an immediate relative (some may require payment of the full change, but refund later when proof is received).

2. Some carriers will offer bereavement fares which are typically not a savings, but do have flexibility and allow for necessarily close-in bookings.

3. Many travel insurance policies will cover varying aspects of these situations. But, just as different carriers have different policies and structures, the same applies to insurance. The only way to know is to carefully read your policy.