This Vulnerability is accepted by LinkedIn they are in a process to patched it but not yet patched. The hack use the Linkedin account deletion page itself.
Vulnerability Information:
Vulnerability Type: ClickJacking
Found By: Asish
Status: UnFixed
Alert Level: Critical
Website: http://linkedin.com
Default Account Closing page provided by Linkedin:
This exploit use the default Account Closing page.User can close his account from LinkedIn by visiting the following page
https://www.linkedin.com/secure/settings?closemyaccountstart=&goback=.nas_*1_*1_*1

Once he click continue user have to click on verify account to close

And Final Step

Exploit:ClickJacking Vulnerability

Once user submit the right answer his account will be removed from LinkedIn
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The document is available here(Password: 8nj98F4h9AW)