Describes a job, position, or task that nobody would want. It is a polite, slightly clever way of saying 'that is a horrible thing to have to do'. Instead of calling the situation bad directly, you say that no one envies the person in it — and the listener works out the rest. It is nearly always followed by a small set of nouns: an unenviable task, an unenviable job, an unenviable position, an unenviable record, an unenviable reputation. That last pair are worth noticing, because there the word turns dry and a little mocking: 'the unenviable record of having lost eleven games in a row' means the record is embarrassing, and the speaker is enjoying saying so. There is real sympathy in the usual use, though. When a newspaper writes 'the coach has the unenviable task of telling the players', it means: this is going to be awful, and we are glad it is not us. It is a formal, journalistic word — very common in news and reports, less common in conversation, where people just say 'I wouldn't want his job'.