When BOTH of the following two conditions are satisfied:
(a) A person fails to attend a planned event (ex. "he totally bailed on the party")
(b) When the event that was "bailed" was super awesome, or at the very least, better than what it was the person "bailed" for. (ex. "bailing on the beach full of hot babes is both a fail and a bail, therefore a bailure?")
Alex tells his friends that he will go to the beach with them. On the beach day, Alex tells his friends he can't go to the beach because he has to take care of his friend's dog. This is the "bail."
If it turns out that the beach was full of hot babes, high-fives, and free pie, the alternative for which Alex passed up the beach is clearly a "fail."
Combined, we have BAILURE (BAIL+FAILURE).