If a person is entitled to rent or compensation, whether such person has the reversion or not, then his personal representative or assignee may recover it as provided in § 8.01-130.1, whatever the estate of the person owning it, or though his estate or interest in the land has ended. When the owner of real estate in fee, or holder of a term, yielding him rent dies, the rent due after such owner’s or termholder’s death shall be recoverable by such owner’s heir or devisee or such termholder’s personal representative. If the owner or holder alienates or assigns his estate or term, or the rent falls due after such alienation or assignment, the alienee or assignee may recover such rent.