Is it possible for a non-Catholic to have confession and receive absolution? In other words is there an instance where a Priest would (or could) decide to hear a confession from someone outside the church?
Canon law (CIC) provides for confession, communion, and annointing of the sick for non-Catholics in certain situations:
“Catholic ministers administer the sacraments of penance, Eucharist, and anointing of the sick licitly to members of Eastern Churches which do not have full communion with the Catholic Church if they seek such on their own accord and are properly disposed. This is also valid for members of other Churches which in the judgment of the Apostolic See are in the same condition in regard to the sacraments as these Eastern Churches. If the danger of death is present or if, in the judgment of the diocesan bishop or conference of bishops, some other grave necessity urges it, Catholic ministers administer these same sacraments licitly also to other Christians not having full communion with the Catholic Church, who cannot approach a minister of their own community and who seek such on their own accord, provided that they manifest Catholic faith in respect to these sacraments and are properly disposed” (CIC 844 §3-4).