Can you give an example? As far as I'm aware, conrotatory and disrotatory is a nomenclature relating only to electrocyclic reactions. By definition, these always involve formation of a new sigma bond from a delocalized pi system, while shortening the pi system by 2 atoms. This means that the terminal atoms prior to cyclization must always be sp or sp2 hybridized so I don't see how "both reactants and products [can] have stereochemistry on the carbon the substituents are attached to" (assuming you don't mean E/Z stereoisomers or chiral allenes). But maybe I'm just not understanding your question...