> db.foo.find({'x.': 1})
{ "_id" : ObjectId("6061e7ac7cc9a947848c1015"), "x" : [ 1 ], "y" : [ { "" : 1 } ] }
{ "_id" : ObjectId("6061e7f27cc9a947848c1016"), "x" : { "" : [ 1 ] }, "y" : [ { "" : 1 } ] }
> db.foo.find({'y.': 1})
>

If we aren't going to error when there is an empty path component, the results should at least make sense. I can't think of any reason (modulo bugs of course) why the first document would match {'x.': 1}. And the second document should either match both or neither of {'x.': 1} and {'y.': 1}. The current behavior where it matches one but not the other is odd.