db.b.find()
{ "_id" : ObjectId("62477ced76646eaf6616e9e3"), "k" : undefined }

db.a.find()
{ "_id" : ObjectId("62477ce276646eaf6616e9e1"), "k" : [ ] }

// no index on collection "a" -- no matches on "undefined"
db.b.aggregate({$lookup:{from:"a", localField:"k", foreignField:"k", as:"matched"}})
{ "_id" : ObjectId("62477ced76646eaf6616e9e3"), "k" : undefined, "matched" : [ ] }

// after creating the index, "undefined" starts matching empty arrays
db.a.createIndex({k:1})
db.b.aggregate({$lookup:{from:"a", localField:"k", foreignField:"k", as:"matched"}})
{ "_id" : ObjectId("62477ced76646eaf6616e9e3"), "k" : undefined, "matched" : [ { "_id" : ObjectId("62477ce276646eaf6616e9e1"), "k" : [ ] } ] }