Etain was apparently once a friend of Destruction's and as such, presumably knew enough about him to know where he might have gone. She was, therefore, in the direct line of fire when Dream and Delirium went on their quest to find their brother. Destruction, by his very nature, had remotely and automatically set fail safes to destroy anyone who might lead back to him.
Etain escaped the gas leak and explosion in her apartment by virtue of some sixth sense, she threw herself out of her apartment window a moment before it exploded, with nothing but her purse and the underwear she had on. She was one of only two from Destruction's past to survive his booby traps.
Delirium later thought Etain had gone into hiding in some far off realm. Who she was and where she went are questions left unanswered.