We investigate the oxidative, thermal conversion of softwood lignin by performing molecular dynamics simulations based on a reactive force field (ReaxFF). The lignin samples are constructed from coniferyl alcohol units, which are connected through linkages that are randomly selected from a natural distribution of linkages in softwood. The goal of this work is to simulate the oxidative stabilization step during carbon fiber production from lignin precursor. We find that at simulation conditions where stabilization reactions occur, the lignin fragments have already undergone extensive degradation. The 5-5 linkage shows the highest reactivity toward cyclization and dehydrogenation.