To safely delete files, folders, or entire drives, PowerShell can use the built-in cipher.exe tool. This line would safely delete the old user profile:
Cipher.exe /w:c:\Users\ObsoleteUser
Note that the path to the folder to delete needs to be separated by a *** from the parameter /w. Clearing the data takes a while: Windows is overwriting the entire data content multiple times to ensure it cannot be recovered.