Sharded $lookup that uses expressive (let-pipeline) syntax can incorrectly match missing local fields to empty object foreign fields. For example, given query:

[
    {
        $lookup: {
            from: coll_foreign.getName(),
            as: "res",
            let: {local_a: "$a"},
            pipeline: [{$match: {$expr: {$eq: ["$$local_a", "$a"]},}}, {$project: {_id: 1}}]
        }
    }
], 

and documents 

{_id: 1, b: 1}, {_id: 2, a: {}} 

within both the local and foreign collection, we would expect to see the following documents in the result set:

{_id: 1, b: 1, res: [{_id: 1}]}, {_id: 2, a: {}, res: [{_id: 2}]}

Instead, we can see

{_id: 1, b: 1, res: [{_id: 2}]}, {_id: 2, a: {}, res: [{_id: 2}]}

Worth looking into whether this serialization error affects non-$lookup cases like those described in SERVER-57403