I believe as per I know, the virus wouldn't live long on a piece of paper If that paper isn't coming in a contact of a person. Let's say that paper got quarantined and gets out of any other's contact so the virus wouldn't last long.
From what I have read, about 3 days. A virus can't survive for too many days if it doesn't "find" someone to infect. So, if you "quarantine" your paper for few days, I guess at the end it will be virus-free.