I have from previous versions of the forum were the directories and files, which in my opinion is not needed.
Here is their list:

cache
hooks
interface
ips_kernel
lofiversion
public
404error.php
constants.php
dav.php
initdata.php

Can you delete everything already? Current version 4.4.6.

404error.php and constants.php are still valid files in IPS4.

If you use friendly URLs, 404error.php is a custom 404 error page used in your .htaccess file.
constants.php is a file used to store "advanced" configuration, such as cache/datastore storage method. 

Thank you! 🧑

It is possible you may have some older content pointing to URLs in the public/ folder (particularly emoticons) so be careful removing that as well.

Otherwise everything else can go (besides what Martin already pointed out)