Board Thread:The Quarters - Q & A/@comment-131.215.167.245-20140209072307/@comment-24150802-20141007015327

To the wikia contributor 108.18.197.36: The comment immediately above yours already answers your question. You are able to get it all back.

Note that equipment from quests are not related to any class. You didn't have to be a specific class to get the equipment in the first place, so you don't have to be a specific class to buy it back after losing it.