A decree of nullity declares that a marriage never existed, whether as a valid and sacramental marriage in the case of two baptized persons, or as a valid but not sacramental marriage in the case in which at least one is unbaptized.
A decree of nullity does not dissolve the marriage but it would have declared the freedom of the party to enter a subsequent marriage. The dissolution of a valid non sacramental marriage by a Pauline privilege or in favor of the faith is an entirely different topic.
As for the original question, the relationship between Church law and moral theology is complex. Both reflect divine law that valid marriage, and certainly a consummated sacramental marriage, is indissoluble.
If a Catholic in a sacramental marriage “received” a decree of nullity after a divorce and subsequent marriage outside the Church, the matter should be brought to the parish priest to address questions of objective sin and culpability through confession, and then “regularizing” the second union according to Church law. There are too many possible complications involved here for responses to be appropriate, and some may be presented that are incorrect.
Beyond that, one can only say that such an attempted marriage outside the Church would not be considered valid by the Church in most circumstances, and that a Catholic would have impaired his or her communion with the Church in some way. Again, this is better discussed with a parish priest.