Recent advances in microwave technology and signal processing have unveiled the potential of the so-called wireless power transfer (WPT) from one device to the other. This has resulted in reducing the need of a local power source at the wireless devices. In this paper, we target a popular physical layer technology, namely the orthogonal frequency division multiplexing (OFDM) and propose a novel approach to prolong the battery life of an OFDM receiver, by exploiting the concept of WPT. We design a novel OFDM receiver architecture that does not discard the cyclic prefix (CP), but instead, exploits it to extract power from the received signal, effectively realizing a WPT between the transmitter and the receiver. The proposed technique does not require any change in the transmission protocol as compared to the legacy OFDM. We show that the amount of power carried in the CP could be made sufficient to decode the information symbols, making the transmission self-sustainable in terms of power consumption at the receiver. We analytically derive the feasibility condition for the self-sustainability of the transmission and analyze its impact on the performance of the OFDM system. Numerical findings provide encouraging results and confirm the potential of the proposed approach.