If you try to search for a specific homeDirectory or profilepath that are assigned to users, you have to filter on this path.
Therefore, let´s assume you have a DFS share named \\domain.com\DFSShare\User and in this share you have all homeDirectories. To find all users using this path you could expect that you can use a query like this:
Get-ADUser -Filter "homedirectory -like '\\domain.com\DFSShare\User*'" -Properties homedirectory | select samaccountname, homedirectory
If you run this line, the output will be empty, even if some users using this share as homeDirectory.
Why? A network path has backslashes and a backslash „\” is a special character. Therefore, if you filter on those paths, you have to replace every \ with \5c.
For more information check out the following MS article:
If we do that our PowerShell query looks like this:
Get-ADUser -Filter "homedirectory -like '\5c\5cdomain.com\5cDFSShare\5cUser*'" -Properties homedirectory | select samaccountname, homedirectory
Now we see all users that have a homeDirectory located in \\domain.com\DFSShare\User