[{"group_id":1,"limit":{"custom:key:a":{"role":"admin","user_id":"user:1"},"custom:key:b":{"role":"moder","user_id":"user:2"}}},{"group_id":1,"limit":{}},{"group_id":2,"limit":{"custom:key:c":{"role":"user","user_id":"user:2"}}}]

db.collection.aggregate([{$project:{_id:1,group_id:1,limit:{$objectToArray:"$limit"}}},{$match:{"limit.v.user_id":"user:2",}}])