If the proceedings are for the financing and improvement of streets and easements initiated under a contract entered into, or proposed to be entered into, between a city, city and county, or county pursuant to Section 66462 of the Government Code and lands which will be subject to assessment for the proposed improvement are encumbered or subject to any existing mortgage or deed of trust, for the purpose of clause (3) of Section 2804, “owners” shall include not only the persons specified in Section 2804 but also any mortgagee or beneficiary under any such existing mortgage or deed of trust. Upon the filing of a petition for any such improvement, the owners, as specified in Section 2804, shall furnish the clerk or secretary of the legislative body with their affidavit, and any additional evidence which the clerk or secretary may require, concerning the existence of all such mortgages or deeds of trust and the names of any mortgagees or beneficiaries thereunder.