This study investigates a new side-channel leakage observed in the inner rounds of an unrolled hardware implementation of block ciphers in a chosen-input attack scenario. The side-channel leakage occurs in the first round and it can be observed in the later inner rounds because it arises from path activation bias caused by the difference between two consecutive inputs. Therefore, a new attack that exploits the leakage is possible even for unrolled implementations equipped with countermeasures (masking and/or deglitchers that separate the circuit in terms of glitch propagation) in the round involving the leakage. We validate the existence of such a unique sidechannel leakage through a set of experiments with a fully unrolled PRINCE cipher hardware, implemented on a field-programmable gate array (FPGA). In addition, we verify the validity and evaluate the hardware cost of a countermeasure for the unrolled implementation, namely the Threshold Implementation (TI) countermeasure.