The intelligent reflecting surface (IRS) can smartly provide supplementary links to improve the wireless propagation environment between the base station and the users. Due to the randomness of user distribution and the limitations of IRS deployment location, it is difficult to guarantee that the propagation loss of all the links constructed by IRS to users at any location can be efficiently compensated. In this paper, a wireless-powered device with ambient backscatter and active transmission acts as a relay to assist in forwarding the IRS reflected signals to extend coverage in the energy constrained conditions. The system ergodic capacity of the proposed model is characterized by deriving the approximate analytical expressions. Furthermore, two types of mode selection mechanisms, namely hard-threshold and soft-threshold for the wireless-powered relay are designed according to the statistical analysis to enhance appropriateness for surrounding signal environment. The accuracy of the theoretical analysis expressions is verified by Monte Carlo simulations. The numerical results show that the proposed model surpasses the scenarios in the case of IRS direct connection, standalone active transmission or backscatter, and the soft-threshold scheme can choose the optimal communication mode in different environments.