To renew the memberships of the members who do not pay is all up to you. You can determine whether the system will cancel the membership automatically or not.
You can assign new payment or cancel membership when not paid.
If you select "Cancel subscription", the system will give you 3 more options.
When you check update organisation membership status, member who did not pay after grace period will have their member status from active to frozen. You can also consider removing the most recent debt added.