Illustrations of the rule against perpetuities

The fertile octogenarian and the unborn widow are two legal fictions from the law of real property (and trusts) that can be used either to invoke the rule against perpetuities to make an interest in property void or, alternatively and much more frequently, to demonstrate the seemingly bizarre results that can occur as a result of the rule. The rule itself, simply stated, makes a future interest in property void if it can be logically proven that there is some possibility of the interest not vesting or failing within 21 years after the end of a life in being at the time the interest is created. 
The fertile octogenarian.
The fertile octogenarian is a fictitious character that comes up when applying the rule against perpetuities. The rule presumes that anyone, even an octogenarian (i.e., someone between 80 and 90 years of age) can parent a child, regardless of sex or health. For instance, suppose that a will devises a piece of land known as Blackacre "to A for her life, and then to the first of A's children to reach 25 years of age." A is, at the time the will is probated, an 85-year-old woman. In applying the rule against perpetuities, an imaginative lawyer will argue (and a court must accept under the common law rule itself) that A could have a child in her 86th year and then in her 87th year all of A's other children could die, then in her 88th year A herself could die. Because the interest will not vest until her new child reaches 25 years of age, which cannot happen until more than 21 years after A and her other children (together who form the "lives in being" to which the rule refers) have all died, the rule against perpetuities makes the entire gift "to the first of A's children to reach 25 years of age" void. A will hold Blackacre for life, and then the property will revert to the person whose will transferred it to A in the first place. (Actually, it will go to that person's estate, since the will was probated only after his death.)
While it is true that there is often no statutory maximum age limit to perform an adoption, and adopted children are often treated the same as natural children, so an 86-year-old woman who adopts a newborn child is legally in the same position as an 86-year-old woman who gives birth, the fertile octogenarian rule predates the laws allowing legal adoption.
The legal fiction of the fertile octogenarian assumes that a living person, regardless of sex, age, or physical condition, will always be capable of having more children, thus allowing an interest to vest 21 years after all the lives in being at the time of the grant are dead. Couples have been known to marry in their late eighties.
In certain places this assumption will be limited to a fixed age set by statute. Furthermore, many jurisdictions have discarded old common-law fictions such as the "fertile octogenarian."
A related legal fiction, which assumes that a living person is fertile at birth, is known as the precocious toddler.
The unborn widow.
The unborn widow poses a similar seemingly silly but logical problem. Suppose that property is left "to A for life, then to his widow for life, then to A's issue." Because the gift to A's widow cannot be resolved until A dies, the law will consider the possibility that, after the property is left to A, he marries a woman who was not born at the time the gift was made. For instance, it is possible that in 1950 the property is left to A, in 1955 a woman B is born, and in 1975 A and B marry each other (neither having issue at the time). Furthermore, it is possible that A will die, say in 1980, and his widow B will outlive him for more than 21 years. Suppose that she dies in 2005. B was not a life in being at the time of the transfer, and the only remaining "validating life" under the rule against perpetuities is A, who has been dead for 25 years by this time. The gift to A's issue does not vest until his widow dies, and since that could theoretically happen more than 21 years after the death of all lives in being at the time of the transfer, the transfer to A's issue is invalid from the start. 
Note that changing the word "issue" to "children" makes the gift valid: Since the class of "A's children" is closed and completely cognizable at the time of A's death (plus a gestation period as allowed by the rule), A's children no longer have a vested remainder subject to open; upon A's death, they now have an indefeasibly vested remainder, which is outside the scope of the Rule against Perpetuities. On the contrary, the class of "A's issue" is subject to expand long after A's death, so their future interest remains that of a vested remainder subject to open, which is within the scope of the rule. B cannot serve as the life in being for A's issue because B was not yet born, i.e., not "a life in being," at the time of the transfer. Because her death could (as explained above) be more than 21 years after A's death, the result is that the gift to A's issue violates the rule because it is possible that the gift will vest more than 21 years after the end of "all lives in being at the time the gift was created".
The problem of the unborn widow is a frequently used illustration of the Rule's complexities. Suppose that a woman, A, wants to devise her estate to her son B and his wife, and then to their children.
A's devise might look something like this:
Though this seems like a reasonable devise, it actually violates the Rule because there is a possibility, however remote, that the interest to "B's children then living" will vest more than 21 years after the deaths of all lives in being.
Suppose B is married without children at the time of the devise. Suppose further that B's wife were to die or B were to divorce. If B were to remarry to someone who was born "after" the devise, the new wife would not be a life in being at the time of the devise. Similarly, any children born to B and his new wife would also not be lives in being at the time of the devise. If B's new wife were to outlive him (making her his widow) and survive him by more than 21 years, then the interest to "B's children then living" would not vest until after the perpetuities period expired (21 years after the death of B, the only relevant life in being at the time of the devise), because only upon the death of the widow can one ascertain who are "B's children then living."
Alternately, if B is not married at the time of the devise and B were to get married afterwards, again the wife could not be a "life in being" since she is not identifiable at the time of the devise. Similarly to the previous case, she could outlive B by more than 21 years, voiding the grant to their children (who also could not be lives in being because they would have been born after the devise was made).
However, if the last interest were simply to "B's children," rather than to "B's children then living," it would vest upon B's death because at that time all of B's children would be ascertainable. In this instance, the devise would be valid under the Rule.
Other examples.
Other hypothetically relevant possibilities which almost never actually occur but have been invoked by lawyers or courts to invalidate transfers under the rule against perpetuities include the slothful executor (a situation where the executor of the estate does not probate the will for many years after the testator's death), the magic gravel pit (a transfer to be made as soon as a gravel pit is out of gravel may not vest for hundreds of years), the war that never ends (a transfer to be made at the end of a war might never happen), and other similar situations.
Criticism and humor.
Because these hypothetical scenarios show how a reasonable gift can be voided based on so unlikely an outcome, they have generated much criticism among legal scholars, resulting in the abrogation of the rule against perpetuities by statute in many jurisdictions. Many U.S. States have adopted laws mollifying the application of the rule by requiring courts to "wait and see" for a period of years, sometimes as long as 360 years (which effectively negates the possibility of litigation ensuing during the life of any person alive at the same time of the author of the will).
Some jurisdictions have ameliorated specific problems of the rule by creating statutory presumptions to counter those problems. Under such statutes, for example, a woman is presumed to no longer be fertile after a particular age (typically 55), and a gift to a person's widow or widower is presumed to vest in whoever was that person's spouse at the time of the gift.
These rules have also long been a target of legal humorists.