When in the case of a lease of real property and the failure of tenant to pay rent, the landlord has a subsisting right to reenter for such failure; he or she may bring an action to recover the possession of such property, and such action is equivalent to a demand of the rent and a reentry upon the property. But if at any time before the judgment in such action, the lessee or his or her successor in interest as to the whole or a part of the property, pay to the plaintiff, or bring into court the amount of rent then in arrear, with interest and cost of action, and perform the other covenants or agreements on the part of the lessee, he or she shall be entitled to continue in the possession according to the terms of the lease.