Maybe run `sudo chmod -R 000 /` instead. Can't get charged with destroying any data, but it's a huge pain to get a system working again from that. Only done it twice; hope never to do so again.
Depending on how you define "fix," the common way (if the machine has already been rebooted and you're locked out of the session) is to boot via a live distro, mount the filesystem, and change permissions to get a usable system back. There are various other methods depending on the machine state and requirements, too, so it's definitely recoverable from a working machine standpoint. Changing permissions back to what they used to be is a rabbit hole that varies depending on your distro, machine-specific requirements, and any special permissions setup by you and your admins.
It's a pain-and-a-half. I'm not sure any system ever recovers fully, but you basically run chmod -R's on most of the important directories and then fix the many services that will surely fail once you can get a shell.
More specifically, I used a bunch of these links until I could get a shell, then manually-fixed the rest.
Can confirm. I kept getting permission errors on something I was testing, and in desperation ran `chmod -R 777` thinking I was in my project dir. I was actually at root. After a bunch attempts to recover, I ended up saving the data I cared about and doing a fresh install. 0/10 would not recommend.