Database
[{"_id":1,"offers":[{"id":12345,"amount":100,"eligibleProducts":[111,123,156]},{"id":12346,"amount":100,"eligibleProducts":[222,333]}]}]
Query
db.collection.aggregate([{$match:{"offers.eligibleProducts":{$in:[111,777,888]}}},{$project:{offers:{$filter:{input:"$offers",cond:{$ne:[{$filter:{input:"$$this.eligibleProducts",cond:{$in:["$$this",[111,777,888]]}}},[]]}}}}}])