If you describe a situation or task as unenviable, you mean that nobody would enjoy dealing with it because it is very difficult, dangerous, or unpleasant.
1. hard to deal with; especially causing pain or embarrassment;
"awkward (or embarrassing or difficult) moments in the discussion""an awkward pause followed his remark""a sticky question""in the unenviable position of resorting to an act he had planned to save for the climax of the campaign"
2. so undesirable as to be incapable of arousing envy;