Consider an energy-harvesting receiver that uses the same received signal both for decoding information and for harvesting energy, which is employed to power its circuitry. In the scenario where the receiver has limited battery size, a signal with bursty energy content may cause power outage at the receiver since the battery will drain during intervals with low signal energy. The energy content in the signal may be regularized by partitioning each codeword into smaller subblocks and requiring that sufficient energy is carried in every subblock duration. In this paper, we study subblock energy-constrained codes (SECCs) which, by definition, are codes satisfying the subblock energy constraint. For SECCs, we provide a sufficient condition on the subblock length to avoid power outage at the receiver. We consider discrete memoryless channels and characterize the SECC capacity, and also provide different bounds on the SECC capacity. Further, we characterize and bound the random coding error exponent for SECCs.