Context. The abundances of many observed compounds in interstellar molecular clouds still lack an explanation, despite extensive research that includes both gas and solid (dust-grain surface) phase reactions. Aims. We aim to qualitatively prove the idea that a hydrogen-poor subsurface chemistry on interstellar grains is responsible for at least some of these chemical "anomalies". This chemistry develops in the icy mantles when photodissociation reactions in the mantle release free hydrogen, which escapes the mantle via diffusion. This results in serious alterations of the chemical composition of the mantle because pores in the mantle provide surfaces for reactions in the new, hydrogen-poor environment.Methods. We present a simple kinetic model, using existing astrochemical reaction databases. Gas phase, surface and subsurface pore reactions are included, as are physical transformations of molecules. Results. Our model produces significantly higher abundances for various oxidized species than most other models. We also obtain quite good results for some individual species that have adequate reaction network. Thus, we consider that the hydrogen-poor mantle chemistry may indeed play a role in the chemical evolution of molecular clouds. Conclusions. The significance of outward hydrogen diffusion has to be proved by further research. A huge number of solid phase reactions between many oxidized species is essential to obtain good, quantitative modeling results for a comparison with observations. We speculate that a variety of unobservable hydrogen-poor sulfur oxoacid derivatives may be responsible for the "disappearance" of sulfur in dark cloud cores.