A person who revived a household can be the head of the family and refer to the name of the abolished family, but won't be given property, so the meaning of restoration of a family is to take over the name and retain the family line such as a head family and a branch family.
再興した者はその家の戸主となり廃絶家の氏を称するが、廃絶家前の財産など各種の権利を引き継ぐ訳ではないため、単に家の名を残し、本家と分家といった家系を残す程度の効果しかない。