A more thorough explanation:

Indefinite failure of issue is a legal term that refers to the fact of a person's dying without any surviving children or other descendants who are eligible to inherit the person's estate. It is also known as dying without issue, definite failure of issue, or default of issue.

For example, if a person dies without any children or grandchildren, their estate would be distributed according to the laws of intestacy, which vary by state. In some states, the estate would go to the deceased person's parents, siblings, or other relatives, while in others, it would go to the state.

The term "indefinite failure of issue" can also refer to a failure of issue whenever it happens, without any certain period within which it must happen. This means that if a person's line of descent comes to an end at any time in the future, their estate would be distributed according to the terms of their will or the laws of intestacy.

Overall, the term "indefinite failure of issue" is important in estate planning and inheritance law, as it determines who will inherit a person's estate if they die without any surviving children or other eligible descendants.