If you want to close a Dropbox profile, you will need a special removal link.
This page will demonstrate you below how we deleted our account using a desktop computer:
1 Open the removal link
by clicking on the green button below.Open Dropbox removal link >
2 Enter your email and password to log in
3 Enter your password
and indicate a reason for leaving Dropbox. You can then click Delete my account when you’re ready.
Your account has successfully been removed. You’ll see a confirmation of it.
Source screenshots (& thanks to): Dropbox.com