This wonderful ironic phrase is used to describe someone who is acting as if Fate has just dealt him or her a terrible blow, when they have, in reality, suffered a minor inconvenience and should just get on with it.
On the other hand, "hard done by" should NEVER be used to describe someone who is trying to recover from a genuinely tragic event.
Friend #1: "I can't believe the way Bob has been acting all hard done by, ever since he had to pay to get his roof fixed."
Friend #2: "it's pathetic all right...."
Friend #3: "I can't believe how hard done by Jessica has been acting lately."
Friend #4: "Well what do you expect? her brother just died! Isn't that kind of low, calling her names when something so terrible has happened?" (storms off.)