SERVER-88087 introduced a rewrite to merge multiple compatible topN/bottomN expressions together to reuse the same sort. However, this rewrite generates the wrong values for missing fields.

Simple repro: for this document: {a: null}, the group below should return {a: null, b1: [null], b2: [null]}; however, it actually returns {a: null, b1: [], b2: []}

{
   $group: {
      _id: "$a",
      b1: {$bottomN: {n: 1, sortBy: {a: -1, b: -1}, output: "$b"}},
      b2: {$bottomN: {n: 1, sortBy: {a: -1, b: -1}, output: "$b"}}
   }
}

With SERVER-88087, this group gets rewritten to:

{                                                  
      '$group': {                                            
        _id: '$a',                                           
        bns: {                                               
          '$bottomN': {                                      
            n: { '$const': 1 },
            output: { b1: '$b', b2: '$b' },
            sortBy: { a: -1, b: -1 }
          }                                                  
        }                                                    
      }                                         
}

In order to recombine the output of the $group to be as expected, we add a project like this at the end:

{$project: {
   _id: true,
   b1: { '$ifNull': [ '$bns.b1', { '$const': null } ]},
   b2: { '$ifNull': [ '$bns.b2', { '$const': null } ]},
}}

The problem is when the value for "b1" or "b2" selected by $bottomN is missing, due to array traversal semantics, the expression '$bns.b1' doesn't evaluate to a missing value, but rather to an empty array.

So, for this document: {a: null}, the original $bottomN would return:

While the rewritten $group would return:
{a: null, bns: [{}]}

And the "$bns.b1" paths in the project would evaluate to [], which would not get converted to a null.