While low-temperature combustion (LTC) strategies have been found to mitigate nitrogen oxides and particulate matter emissions in diesel engines, studies have also associated LTC with an increase in unburnt hydrocarbons. With more recent studies on diesel after end-of-injection (AEOI), combustion recession is identified as a phenomenon where at near nozzle region, high-temperature ignition (HTI) combustion can propagate back to the nozzle tip consuming the unburnt hydrocarbons AEOI. Current literature has suggested that combustion recession is controlled by auto-ignition. However, high-fidelity simulations and detailed analysis of such a mechanism are missing. In this study, comprehensive Large Eddy Simulations of a reacting spray at "Spray A"conditions are performed, where detailed analysis of combustion recession concerning flame morphology and propagation modes are included. In particular, this study demonstrated for the first time that while combustion recession is mainly auto-ignition dominated (consistent with the literature), a cool flame was found to deflagrate towards the richer regions of the mixture, promoting mixing and increasing the mixture temperature. This leads to HTI kernels, which then grow and develop as deflagrative waves, therefore sustaining the combustion recession process. The study also detailed the extinction mechanism of combustion: the entrainment wave will overlean the near-nozzle mixtures, rendering it unable to support HTI, which leads to the extinction of the upstream flame AEOI in lower reactivity mixtures. Combustion recession is also observed to be contingent on the chemical and diffusion processes, even at low scalar dissipation rates. Finally, a new criterion for combustion recession based on chemical explosive mode is proposed and validated with previous combustion recession index to quantify the extent of HTI in near-nozzle mixtures AEOI. The newly developed metric combined with a previous experimentally-based metric can provide simple but valuable measurements of the degree and propensity of the upstream flame AEOI. Novelty and Significance Statement This work covers the literature gap in detailing the spray after end-of-injection combustion recession mechanisms. The study is significant, suggesting that while combustion recession is auto-ignition-dominated, deflagration modes were found, for the first time, to exist within the kernels via a cool flame at the end of injection. With further analysis, the deflagration modes were found to promote mixing at the end of injection which is deemed critical in sustaining combustion recession. The extinction mechanisms on the other hand were associated with the significant role of entrainment waves after end-of-injection. To generalize the findings of our study, a novel combustion recession metric based on the chemical explosive mode is proposed where agreement is found with the experimental observations. The new metric can provide an effective computational diagnostics tool for 3-D numerical simulations which complements the previous experimental metric in identifying the propensity and degree of combustion recession.