Single-atom catalysts (SACs) are rapidly developing in various application areas, including electrocatalysis of different reactions, usually taking place under harsh pH/electrode potential conditions. Thus, a full atomic-level understanding of the nature of the active sites under realistic electrochemical conditions is needed, having in mind that the state of SACs active centers could be altered by the adsorption of spectating species. In this contribution, Density Functional Theory is employed to conduct thermodynamic analysis of SACs with metal atoms (Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt, or Au) embedded into N4 moiety in graphene. Various surface electrochemical processes on such SACs are considered, their Pourbaix plots are constructed, and their activity, selectivity, and stability under operating conditions are discussed. It is demonstrated how adsorption of H, O and OH can cause blockage and restructuring of the active sites and alter the electronic structure. Furthermore, when one deals with metals with lower D-band filling, it is shown that metal center oxidation is preferred over the oxidation of carbon lattice. The effect of the state of the metal center on the reactivity of the carbon lattice is discussed in the case of Fe@N-4-graphene. Finally, a possible strategy for confirming the changes in the architecture of the SACs' active site by analyzing their vibration spectra is suggested.