I suppose it’s safe to assume you are using a most restrictive ACL model from top down? Assuming that and also that everyone gets notified when something is deleted (a global setting) there are a few hacks you can do but nothing OOTB for Box.
So from a prevention perspective, here is what I have done in the past. In any folder that you do not want to be moved or deleted, place a text (or Word) file called something innocuous like “Placeholder” or something in that folder. Then, using a service account in a VM or some laptop shoved in the corner, assign editor rights to that service account and invite them to that folder. Then install Box Drive on that VM/spare laptop and open up that file locally from Box Drive and just leave the file open forever. No one can modify that folder from then on.
You can also set up a Box Relay to create a Move event (you can do delete event too but if you already have global delete notifications turned on it’s not necessary). Whenever someone moves a folder you (or anyone else) can be emailed that it happens. While it’s not preventative per se, it’s the only way I’ve found to be notified when a folder moves that I care about.