waiving goodbye
The act of not requiring someone to bid one or more other humans farewell if doing so would be too emotionally distressing. Or the uncomfortable person himself decides to just "sneak out early" before others are awake to observe his departure, so that he doesn't have to endure the whole "long tearful parting" crap that would otherwise be "socially mandatory" if the other folks knew he was leaving.
A prime example of "waiving goodbye" is related in the classic "origin of the yodel" joke: the traveler heads out "at first cock's crow" from the farmer's barn where he'd been sleeping overnight, so that there wouldn't be any embarrassing --- and possibly dangerous! --- explaining to do if the farmer's wife and/or daughter decided to do any joyful "crowing" of their own about the wonderful things that the traveler had performed with his own "cock" on them the previous evening when they had separately gone out to the barn to bring him food and wine for his supper.