Conn. Gen. Stat. § 49-18: Foreclosure by executor, administrator or trustee.

When any executor, administrator or trustee obtains a decree of foreclosure, the premises foreclosed, or the proceeds thereof if sold by him, shall be held by him in the same manner and for the benefit of the same persons and to be used for the same purposes and subject to the same rules as the money secured by the mortgage would have been if collected without foreclosure. If such premises are not sold by him, the same shall be distributed, or otherwise disposed of, to the persons who would have been entitled to the money if collected.