Commentary for Kiddushin 125:14

The first part of this mishnah is straightforward. Slightly more complicated is the second part. If the father dies, he cannot consent to the betrothal. Nevertheless, the mishnah rules that she is betrothed. The assumption is that when the man said “on condition that my father consents” he really meant to say, “on condition that my father does not disapprove.” Since after his death the father cannot disapprove, the betrothal is valid. If the son dies, the mishnah finds a convenient way for the woman to avoid the need for yibbum (levirate marriage to her husband’s brother). The court would instruct the father to state that he did not approve of the marriage and he would thereby annul the betrothal. If the betrothal was annulled, the woman would not be liable for yibbum.