Bioenergy with carbon capture and storage (BECCS) offers a unique opportunity to realize net-negative emissions, such that the system actively removes CO2 from the atmosphere, while also producing reliable base-load electricity. To achieve net-negative emissions, BECCS requires minimal indirect emissions and the low-cost separation of CO2 from other gases. Molten sorbents represent a newly discovered and highly efficient class of material for this separation and could therefore improve the feasibility of BECCS. This work identifies that, relative to coal, bioderived feedstocks provide modest technical advantages for molten sorbents and that regeneration driven by steam remains effective at the pilot scale. Depending on the fuel, BECCS could remove 300-850 kg of CO2 equivalent from the atmosphere per megawatt hour of electrical output (kg/MWh(e)). The levelized cost of electricity (LCOE) was found to depend heavily on the biomass feedstock cost, which varies considerably. Early adopters could utilize low-cost resources and play an outsized role in climate change mitigation. However, the total addressable market is limited by the availability of land, water, and nutrients. The estimated cost of CO2 avoided using molten salt sorbents and was $45-50/tonne relative to coal and $80-100/tonne relative to the future, largely renewable, electrical grid. This emphasizes the resilience of BECCS to competition from other low carbon technologies, the low costs of molten sorbents compared to other sorbents, and the opportunity to offset emissions from hard-to-abate industries.