The option is now available in the Business Edition

I have a beta version of the upgrade available for you. It includes the transfer function that you are looking for.
Please get yourself the current Business Edition. I will see your order and will email the install package of the beta upgrade to you, for you to evaluate.
Before the upgrade is officially released, some more fine-tuning is required.

No, the current editions of the plug-in does not transfer user groups, they only disable and/or
remove accounts.
But this is an interesting option for a future upgrade. It will include a standard 'downgrade' - after the set time limit has passed - from some user group X to 'registered' and it will be released shortly, but... for the Business Edition only.

Message received via email and posted here for others to learn the answer:

Can the JUser BestBefore plug-in transfer a user from say "Paid" group to "Registered" group
after 1 day or so?
Because I need that kind of feature.