The electric power sector must be deeply decarbonized at a reasonable cost to achieve economy-wide decarbonization goals via sustainable electrification of other sectors. While variable renewable energy generation is expected to dominate grid decarbonization efforts, variability creates the need for supply- and demand-side technologies that can operate flexibly to balance the system. This paper proposes a new concept for power plant flue gas capture integrated with a novel lime-based direct air capture technology to enable flexible operation of the power plant and achieve negative emissions under all operating scenarios. Steady-state models are developed, and sensitivity analyses are conducted on key process variables to investigate system performance. The results, presented at three different power plant loading levels (100 %, 40 %, and 0 %), demonstrate negative emissions of -0.188 tCO2/MWh at 100 % loading and -2.087 tCO2/MWh at 40 % loading. Economic modeling suggests the need for carbon credits exceeding $170/tCO2 to achieve positive net present values.