Exiting out of Private Browsing mode of Firefox erases all of your tracks and data during that session including anything currently stored on the clipboard that was coppied during that session.

Example scenario:

1) Start private browsing
2) Visit banking website or similar
3) Receive a receipt number for the transaction
4) "Copy" the receipt number
5) Exit private browsing mode
6) Paste receipt number in notepad etc

You will find in step 6 that you will paste nothing.