If any person required to list property for taxation and provide the assessor with the list, is prevented by sickness or absence from giving to the assessor such statement, such person or his or her agent having charge of such property, may, at any time before the close of the session of the board of equalization, make out and deliver to said board a statement of the same as required by this title, and the board shall, in such case, make an entry thereof, and correct the corresponding item or items in the return made by the assessor, as the case may require; but no such statement shall be received by the said board from any person who refused or neglected to make oath to his or her statement when required by the assessor as provided herein; nor from any person unless he or she makes and files with the said board an affidavit that he or she was absent from his or her county, without design to avoid the listing of his or her property, or was prevented by sickness from giving the assessor the required statement when called on for that purpose.