If a subscription product is scheduled to be closed at a future date but is renewed before that date, does the renewal line get terminated at the scheduled future date?

No, the renewal line of a product doesn't get terminated at a scheduled future date when the product is scheduled to be terminated or closed.

A renewed subscription is self sustained and isn't affected by its previous version. To know more about relationship subtabs between source and renewed subscriptions, see how do I automatically or manually renew Subscriptions?