"Decomposing" is what "a-mouldering" means, but I'm not sure what the "a-" is called. There is in Greek a usage called "alpha privative" where the "a" prefix means "without, -less, not" as in "agenes" = ignoble, from "a- + genos = family, kindred" or "agnotos" = unknown, new, from a- + gnotos = known".

This would seem to be a usage going in a different direction. The a- prefix in English generally connotes duration, or a prolonged or continued action, the same idea which is conveyed in other Indo-European langues by the imperfect tense. But I still don't know what it's called.