Do the people in question have a responsibility to state they are living chastely to those that know that they shouldn’t be receiving if they aren’t living chastely? Do those people that know it isn’t right if they aren’t living chastely have a responsibility to bring it up to them or tell the priest or what? If the priest is told that they are living chastely, does he then have a responsibility to tell that to those that bring the situation to his attention, or direct them to ask the couple or what?
I guess all this presumes nothing is said about it in confession of course.
Freegards
I don’t know what you mean by “presumes nothing is said about it in Confession.” A priest cannot speak about or act on anything he learns in Confession.
A couple who are living together but have no right to conjugal relations must abstain from such relations. If they are doing so, they may receive Communion. They have an obligation not to cause scandal when they receive Communion. Scandal can be avoided by receiving Communion where they are not known at all, or by informing those whose business it is that they are living chastely.
If I were a pastor with such a couple in my parish, and another parishioner were to bring it up, I would tell him he has no reason to be concerned.