Section 4. A party against whom, without other notice than publication in a newspaper, a judgment or decree has been rendered under section two and whose right is barred thereby, may recover from the person in whose favor such judgment or decree was entered, or from his executors, administrators, heirs or devisees, in accordance with chapter one hundred and ninety-seven, the value at the time action is brought of any interest or right, except of improvements made by the defendants, of which he may have been deprived by such judgment or decree, unless at that time an action which, but for such judgment or decree, he might have maintained for the recovery of such interest or the enforcement of such right would have been barred by the statute of limitations.