Having lost one, you can't erase the fact (6)
I believe the answer is:
rubber
'fact' is the definition.
Although both the answer and definition are singular nouns, I cannot see how one could define the other.
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for rubber that I've seen before include "It can remove so-called lead" , "tough polymeric material?" , "Boring, obsessive type" , "Stretchy substance" , "item in 27 [BRIDGE]?" .)