I only assume that the first marriage was valid. If the first marriage was valid, then they cannot be considered as spouses. They should be commended for their continuance. However, we also have to consider the aspect of public scandal, especially if the faithful are aware of her divorce. If they are living together, they are both identified as a couple, despite their continence ways of life. Despite their heroic choice of living in continence, they cannot speak of it publicly, and the faithful will refuse to believe this because, whether they like it or not, matrimony in a cultural and ecclesial sense is a public matter.
They have to appeal to the Church to receive communion; the Church allows these specific cases. As John Paul II wrote in his exhortation entitled Familiaris Consortio, He said, "A very valuable witness can and should be given by those husbands and wives who, through the joint exercise of periodic continence, have reached a more mature personal responsibility about love and life." He also added, "Reconciliation in the sacrament of Penance which would open the way to the Eucharist, can only be granted to those who, repenting of having broken the sign of the Covenant and of fidelity to Christ, are sincerely ready to undertake a way of life that is no longer in contradiction to the indissolubility of marriage." This means, in practice, that when, for serious reasons, such as the children's upbringing, a man and a woman cannot satisfy the obligation to separate, they "take on themselves the duty to live in complete continence, that is, by abstinence from the acts proper to married couples."
Most importantly, they need to pray and reflect on whether they should still live under one roof, provided they are not married by God and his Church. This kind of lifestyle is also very antithetical to the Gospel. They could also stay as friends, or if they have common children, they need to find a constructive solution. Lastly, I would advise them to pray and seek guidance from the Holy Spirit to be enlightened by the logic of the Gospel.
Dear visitors of Gloria Dei and all who have already written or who will write a personal message to me. I am grateful for your attention, your kindness, for your spiritual support and especially for your sacrifices and prayers for me. God may reward you!
