Are sure that your cloud provider is giving you the ability to completely remove personal information when required? This article highlights some of the difficulties that may be encountered. 

Infopreserve, a Rochester, NY cloud provider, recognized the issue from the very beginning and has dealt with it accordingly. According to Clive Daunton, VP of Product Development, "When a user marks a file for deletion and it is approved by an administrator the file is moved to the deleted files folder. That night the file is erased by overwriting 7 times to the DoD 5220.22-M specification. On a monthly basis the backups are updated to erase the deleted files from the backups." 
It's important to always be sure that your contractors comply with all relevant laws and regulations.
John Brokaw, CRM, CIP
GLC National Records Director