In any case in which the board of supervisors determines, after investigation, that the purposes of this part will be served by releasing or subordinating any lien in whole or in part or reconveying or subordinating in whole or in part any interest or estate transferred or granted to the board of supervisors under the provisions of Section 17109 or under the provisions of Section 9 of an act entitled “An act to provide for the aid and relief of indigents,” approved June 5, 1933, and determines that the property affected by such lien, transfer or grant, except such interest or estate as may have been conveyed to the county, is at the time owned by the recipient of aid, the board of supervisors may release such lien in whole or in part or may reconvey such interest or estate in whole or in part or may subordinate the lien, interest or estate so transferred or granted to it to one or more designated encumbrances executed by the recipient of aid, without consideration or for such consideration as the board may determine.