No you can’t just attach it to a new VM account and it will eventually be deleted along with all the messages in it - this really should be done some 90 days after the original account is closed. As the original account was never yours, I doubt VM will allow you to simply take over the address and mailbox for security reasons.
All I can suggest is that you use an email client to download all the the existing messages, create a new email address for yourself, import the existing mail into this new mailbox and setup a forwarder on the old mailbox to forward new mail to the new account for however long the old address lists for, could be months or even years but eventually it will go.
I would also suggest that to avoid these issues occurring again in the future, you seriously consider getting an email account not tied to an ISP (outlook or gmail etc.) which will be ‘yours’ indefinitely irrespective of which ISP you are using.
It is indeed at risk if your parents are no longer VM customers; because they were the account controllers, they and not you are responsible for the state of the account and keeping it in good order. For as long they remain customers they will be able to access the address and change its password. You will not be able to access it to do any of the account management things you might like to do.
If they ever leave VM or have left VM already then while the account may still be available to you it will count as an orphan account. Read this to see what that means:
It is not possible to detach the address from your parents VM account and join it to your new account. Only the whole set of their addresses could be moved. So they would be without e-mail and you would get all their addresses. Not a place either party would wish to go?
Advice - stop using it. Create a proper new virginmedia.com address on your VM account so you can have the full responsibility for managing it and tell your contacts about the change.
I'm a Very Insightful Person, I'm here to share knowledge, I don't work for Virgin Media. Learn more
Have I helped? Click Mark as Helpful Answer or use Kudos to say thanks