Power system reliability assessment quantifies the impact of component failures on supply capability, providing an important basis for system planning, operation scheduling, and risk management. State enumeration produces deterministic and interpretable results; however, due to the combinatorial explosion of the state space, only a limited number of low-order states can usually be analyzed in large-scale systems. This leads to loose lower bounds of reliability indices and underestimation of system risk. To improve the accuracy of reliability-index lower bounds under a finite set of analyzed states, this paper proposes a reliability lower-bound assessment method based on tail-probability reconstruction of load shedding. Under the engineering monotonicity assumption of load shedding, the proposed method infers load-shedding information of related higher-order unanalyzed states from the component-outage sets and load shedding of analyzed states, and reformulates reliability indices from a state-by-state weighted form into a tail-probability form over load-shedding thresholds. Furthermore, minimal failure-set simplification, binary decision diagram-based exact probability calculation, and an incremental updating mechanism are combined to efficiently construct tail-probability lower bounds and calculate reliability indices. Case studies show that, under the same computation time, the proposed method preserves the lower-bound property and obtains more accurate reliability indices than traditional state enumeration.