Taxing districts shall at all times make exonerations for uncollectible occupation, poll and per capita taxes, mistakes, indigent persons, unseated lands, deaths, removals, et cetera, as to them shall appear just and reasonable. The chief clerk or secretary, as the case may be, of each taxing district shall enter in a book or books, to be kept for that purpose, the names of all persons exonerated, together with the reason why, the amount of the tax, and date when made, and give to the tax collector a certificate directed to the proper treasurer, stating the nature of the tax and the amount exonerated in order to make settlement accordingly. The list of exonerations shall remain in force until the taxing district upon information received from the tax collector or for other valid reasons, shall rescind or change the list. When a tax collector has been exonerated from the collection of any tax, such action shall not in any way have the effect of discharging or limiting the liability of the taxable, but all methods of enforcing collection of taxes shall continue as though no exoneration had been made.