It took me forever to figure this out so thought I'd post the solution.
Restoring a file you deleted (locally) while working in Box Drive
I am the admin for our account, so this works for me as Admin.
Login to Box through a browser and go to Admin area.
Go to Content > Content Manager
Click on the user name who deleted the files or filter to the user name
At the bottom of their files there is a TRASH folder. Click on it.
Most-recently-deleted files will be at the top. Checkmark the ones you want to recoever then click RESTORE.