Nothing strange about this word for looking exhausted and unwell, you may think, but it’s a classic case of a word which has changed its sense remarkably in the course of its history.
When it first came into the language in the sixteenth century, a haggard was a hawk that had been caught for training after it had taken on its adult plumage (this meaning is still extant in falconry). Adult hawks are hard to tame, so it came to mean anything wild or feral.
It was only about 1580 that we start to see it applied to people, at first to wild-looking or intractable individuals. Shakespeare uses both senses in a bit of wordplay in Othello in which Othello is musing about the imagined unfaithfulness of his wife Desdemona: “If I do prove her haggard, / Though that her jesses were my dear heartstrings, / I’d whistle her off and let her down the wind / To prey at fortune”. Later still it was assumed that anybody who looked wild was suffering the effects of privation, fatigue, terror or worry — hence unwell.
The source of haggard isn’t known for sure: it’s certainly from French hagard, but where that comes from is open to some doubt. We are pretty sure, though, that the English hag for an ugly old woman had some influence on the shift to the modern meaning, through people thinking that haggard was in some way linked to it.