Adoption was very common, and acceptable.

In the western tradition, we think that the family may only be continued by a blood relation, but this wasn't necessarily true in China. During the Song/Yuan/Ming period (~AD 960-1644) an heirless family had two adoption options to continue the line.

One, they could adopt a younger family member from another branch of the lineage (such as a nephew, or the son of a cousin) with the permission of the biological father to serve as a replacement heir. This could be done no matter what age the new heir currently was, be he a newborn or a grown man.

Sometimes, however, even this was not possible. In these cases it was considered perfectly acceptable and legitimate to adopt a new male heir from outside the family to continue the line. But in this case it was legally required that the adopted heir be taken in by his new family and raised by them from a very young age. It would not have been legitimate or legal to adopt someone from outside the family if they were already an adolescent or a grown man.

It was extraordinarily rare for a woman to adopt her father's holding in her own right. To do so would have been unfilial due to the impossibility of continuing the family name. It was sometimes possible for a woman to marry a man and have that man be integrated into her family rather than the other way around. But this was frowned upon and uncommon.