Database

[{_id:ObjectId("6386ef039775398be3620c76"),firstName:"A",lastName:"BA",age:34,history:[{disease:"fever",cured:true},{disease:"malaria",cured:false}]},{_id:ObjectId("6386ef239775398be3620c77"),firstName:"AA",lastName:"BA",age:24,history:[{disease:"cold",cured:true},{disease:"thyroid",cured:false}]}]

Query

db.collection.aggregate([{$match:{history:{$elemMatch:{cured:false}}}},{$set:{history:{$filter:{input:"$history",cond:{$eq:["$$this.cured",false]}}}}}])

Result