Objection 1. It would seem that affinity does not remain after the death of husband or wife, between the blood-relations of husband and wife or "vice versa." Because if the cause cease the effect ceases. Now the cause of affinity was the marriage, which ceases after the husband's death, since then "the woman... is loosed from the law of the husband" (Romans 7:2). Therefore the aforesaid affinity ceases also.
Objection 2. Further, consanguinity is the cause of affinity. Now the consanguinity of the husband with his blood-relations ceases at his death. Therefore, the wife's affinity with them ceases also.
On the contrary, Affinity is caused by consanguinity. Now consanguinity binds persons together for all time as long as they live. Therefore affinity does so also: and consequently affinity (between two persons) is not dissolved through the dissolution of the marriage by the death of a third person.
I answer that, A relation ceases in two ways: in one way through the corruption of its subject, in another way by the removal of its cause; thus likeness ceases when one of the like subjects dies, or when the quality that caused the likeness is removed. Now there are certain relations which have for their cause an action, or a passion or movement (Metaph. v, 20): and some of these are caused by movement, through something being moved actually; such is the relation between mover and moved: some of them are caused through something being adapted to movement, for instance the relations between the motive power and the movable, or between master and servant; and some of them result from something, having been moved previously, such as the relation between father and son, for the relation between them is caused not by (the con) being begotten now, but by his having been begotten. Now aptitude for movement and for being moved is transitory; whereas the fact of having been moved is everlasting, since what has been never ceases having been. Consequently fatherhood and sonship are never dissolved through the removal of the cause, but only through the corruption of the subject, that is of one of the subjects. The same applies to affinity, for this is caused by certain persons having been joined together not by their being actually joined. Wherefore it is not done away, as long as the persons between whom affinity has been contracted survive, although the person die through whom it was contracted.
Reply to Objection 1. The marriage tie causes affinity not only by reason of actual union, but also by reason of the union having been effected in the past.
Reply to Objection 2. Consanguinity is not the chief cause of affinity, but union with a blood-relation, not only because that union is now, but because it has been. Hence the argument does not prove.
Source: Summa Theologica (New Advent)