What you are looking for is called process accounting.
The link above gives instructions on setting up process accounting for red hat, ubuntu or debian and some examples on usage.
Note: Process accounting does not prevent the person(s) from repeating the act. It's up to the sysadmin to secure the file
system to the best of his/her knownledge.
The user can protect their home folder by doing chmod -R 700 on their home folder.
If they wish to share a folder with a group or everyone on the system, he/she can add the sticky bit to the folder which allows a user to delete their own files and no one else.