If Delta files bankruptcy it will most likely be a Chapter 11 reorganization, which means they get protection from their creditors, not a Chapter 7 liquidation, which means they would cease operations.
Traditionally, if airlines have ceased operations, other airlines will honor their tickets on a space-available basis with a small fee. There hasn't been a MAJOR airline cease operations in many years, so its difficult to say what would happen if a major stopped flying.
Bottom line, if Delta files bankruptcy, they're still going to be flying. Heck, United has been in bankruptcy protection for over 2 years now.