They're non-existent when given away (7)
I believe the answer is:
secrets
I'm afraid I can't even guess how this answer relates to the clue.
Can you help me to learn more?
(Other definitions for secrets that I've seen before include "Undivulged facts" , "They're not to be disclosed to others" , "Confidential data" , "Mysteries" , "Concealed facts" .)