db={"collection_a":[{id:"a1",collection_b:["b1","b2"]},{id:"a2",collection_b:["b2"]},],"collection_b":[{id:"b1",isOpen:true},{id:"b2",isOpen:false},{id:"b3",isOpen:false}]}

db.collection_a.aggregate([{$lookup:{from:"collection_b",let:{collection_b:"$collection_b"},pipeline:[{$match:{$and:[{$expr:{$in:["$id","$$collection_b"]}},{isOpen:true}]}},{$group:{_id:null,id:{$first:"$id"}}}],as:"collection_b_result"}},{$match:{collection_b_result:{$ne:[]}}},{$project:{collection_b_result:0}}])