Adsorption of CO2 from post-combustion flue gas is one of the leading candidates for globally-impactful carbon capture systems. This work highlights opportunities and limitations of sub-ambient CO2 capture processes utilizing a multi-stage separation process. A hybrid process design using a combination of pressure-driven separation of CO2 from flue gas followed by CO2-rich product liquefaction to produce high purity (>99%) CO2 at pipeline conditions is considered. The economic viability of applying pressure swing adsorption (PSA) processes using fiber sorbent contactors with internal heat management were found to be most influenced by the productivity of the adsorption system. Three exemplar fiber sorbents (MIL-101(Cr), UiO-66, and zeolite 13X) were considered for application in the sub-ambient process of PSA unit. MIL-101(Cr) and UiO-66 fiber composites were estimated to have costs of capture as low as $61/tonne CO2.