Conn. Gen. Stat. § 49-19: Title to vest in encumbrancer paying debt and costs.

In actions of foreclosure, when a judgment of strict foreclosure is rendered and there are subsequent encumbrances, the judgment may provide that, upon the payment of the debt and costs by any encumbrancer, after all subsequent parties in interest have been foreclosed, the title to the property shall vest absolutely in such encumbrancer making such payment, subject to such unpaid encumbrances, if any, as precede him.