Database
[{"_id":ObjectId("56f277b1279871c20b8b4567"),"stores":[{"_id":ObjectId("56f277b5279871c20b8b4783"),"offers":[{"_id":ObjectId("56f277b1279871c20b8b4567"),"size":["XS","S","M"]},{"_id":ObjectId("56f277b1279871c20b8b4567"),"size":["S","L","XL"]}]}]}]
Query
db.collection.find({"stores.offers.size":"L"},{"stores":{"$filter":{"input":{"$map":{"input":"$stores","as":"store","in":{"_id":"$$store._id","offers":{"$filter":{"input":"$$store.offers","as":"offer","cond":{"$setIsSubset":[["L"],"$$offer.size"]}}}}}},"as":"store","cond":{"$ne":["$$store.offers",[]]}}}})