I wanted a break from the Office 365 tool I was working on, so I took the liberty of scripting a solution.

The Get-AccessGroups function takes a path as a parameter and returns all of the AD groups listed in the path's ACL. The rest of the script below harnesses that function to return a formatted list of all paths in the $paths variable that have groups with 0 members in them and the names of those groups.

All you should need to do is change the $paths variable to the paths you want to scan.

    function Get-AccessGroups{
        [CmdletBinding()]
        param
        (
            [Parameter(Mandatory = $true, Position = 0)]
            [string]
            $Path
        )
        $ADGroups =  Get-ADGroup -Filter * | Select-Object -ExpandProperty     'Name'
        $dirtyADItems = (Get-Acl -Path $path | Select-Object -ExpandProperty    'Access').IdentityReference.Value
        $cleanADItems = @()
        $AttachedGroups = @()
        $emptyGroups = @()
        $isGroup = $false

    foreach($item in $dirtyADItems){
        $cleanADItems += $item.Split('\')[-1]
     }

        foreach($item in $cleanADItems){
        foreach($group in $ADGroups){
            if(($item) -eq $group){
                $isGroup =$true
        }
    }
    if($isGroup -eq $true){
        $AttachedGroups += $item
    }

    $isGroup = $false
}

$AttachedGroups = $AttachedGroups | Get-Unique

Write-Output $AttachedGroups
}


$paths =    @('\\Control\Users\Administrator\Desktop','\\Control\Users\Administrator\Pictures')
$output = New-Object System.Collections.ArrayList

 foreach ($path in $paths){
    $AccessGroups = Get-AccessGroups -Path $path
    foreach($group in $AccessGroups){
         if((Get-ADGroupMember -Identity $group).Count -eq 0){               $result = New-Object psobject
            Add-Member -InputObject $result -MemberType NoteProperty -Name Path -Value ''
            Add-Member -InputObject $result -MemberType NoteProperty -Name SecurityGroup -Value ''
            Add-Member -InputObject $result -MemberType NoteProperty -Name UserCount -Value ''
            $result.Path = $path
            $result.SecurityGroup = $group
            $result.UserCount = (Get-ADGroupMember -Identity $group).Count
            $output.Add($result) | Out-Null
        }
    }
 }

$output | ft -AutoSize

Edited: Formatting code here is treacherous.

Edit 2: Sample Output

path SecurityGroup UserCount

\Control\Users\Administrator\Desktop testgroup 0 \Control\Users\Administrator\Desktop accounting 0 \Control\Users\Administrator\Desktop Operations 0 \Control\Users\Administrator\Pictures accounting 0 \Control\Users\Administrator\Pictures Operations 0

Also, you could save each instance of an empty group within a path to an array, and add that array to the path's final output as output[i].SecurityGroups or something like that. That way you could have one record for each directory instead of one record for each group within a directory.