[FeFe] hydrogenases are H2-evolving enzymes that feature a diiron cluster in their active site (the [2Fe]H cluster). One of the iron atoms has a vacant coordination site that directly interacts with H2, thus favoring its splitting in cooperation with the secondary amine group of a neighboring, flexible azadithiolate ligand. The vacant site is also the primary target of the inhibitor O2. The [2Fe]H cluster can span various redox states. The active-ready form (Hox) attains the Fe(II)Fe(I) state. States more oxidized than Hox were shown to be inactive and/or resistant to O2. In this work, we used density functional theory to evaluate whether azadithiolate-to-iron coordination is involved in oxidative inhibition and protection against O2, a hypothesis supported by recent results on biomimetic compounds. Our study shows that Fe-N(azadithiolate) bond formation is favored for an Fe(II)Fe(II) active-site model which disregards explicit treatment of the surrounding protein matrix, in line with the case of the corresponding Fe(II)Fe(II) synthetic system. However, the study of density functional theory models with explicit inclusion of the amino acid environment around the [2Fe]H cluster indicates that the protein matrix prevents the formation of such a bond. Our results suggest that mechanisms other than the binding of the azadithiolate nitrogen protect the active site from oxygen in the so-called H ox (inact) state.