Chemical looping combustion (CLC) enables efficient combustion of hydrocarbon fuels while also producing a gas stream with high CO2 concentrations, suitable for carbon capture and storage (CCS). CLC of biomass in combination with CCS results in efficient removal of carbon dioxide from the atmosphere, i.e., negative emissions. However, biomass and waste-derived fuels can contain significant fractions of aggressive ash precursors, which can affect the operability and functionality of oxygen carriers. In this paper, the fate of common ash elements will be investigated thermodynamically in a system utilizing iron-based oxygen carriers: ilmenite and iron oxide. Multiphase, multicomponent equilibrium calculations were performed using databases from FACT and a user-defined database, with a specific focus on alkali (K and Na) and heavy metals (Cu, Zn, and Pb). A detailed and comprehensive comparison with available literature data from experimental investigations was performed, and compounds not available in the databases were identified. Due to a lack of thermodynamic data in the literature, thermodynamic properties for four compounds, K0.85Fe0.85Ti0.15O2, K0.4Fe0.4Ti0.6O2, KTi8O16, and KTi8O16.5, were obtained from first-principles calculations. The fate of ash elements is studied for CLC of three biomass and waste-derived solid fuels under relevant CLC conditions: 950 °C in the fuel reactor and 1050 °C in the air reactor. Results show that the choice of the oxygen carriers largely influences the behavior of the ash elements. Compared to CLC with iron oxide, ilmenite is more beneficial with respect to high-temperature corrosion since less potassium is released into the gas phase since the titanium content in ilmenite immobilizes both potassium and calcium. For both oxygen carriers, the most corrosive compounds are expected to leave with the gas in the fuel reactor, keeping the air reactor free from chlorides. It was found that the compound KTi8O16 is stable in reducing conditions and low potassium concentrations. This is in conformity with previous experimental data, where this phase has been identified in the interior of ilmenite particles used in oxygen carrier aided combustion of wood chips.