No. The court will appoint an administrator or administratrix with will annex if no executor is appointed or if the appointed one declines to accept.
In America, if there is no living relative when one dies intestate the property is escheated to the county of the state wherein the deceased was domiciled. State laws may vary, but the state or the county will acquire title. If one dies testate, I cannot visualize a situation wherein the property will be escheated, even in the unlikely scenario of the OP.
Personally, I would have told her to quietly ignore that stipulation. After all, who’s going to care? Or if she wanted to follow the will but not kill the dogs, she could have waited until the dogs died naturally and then had them cremated and buried next to her aunt.
As far as Howard Hughes that someone else brought up, Cecil has a column on him which I’m too lazy to dig up right now. According to Cecil, the big fooforaw with him was that he died intestate – the richest person in the US to do so.
And for the OP, if the righ person really didn’t want anyone to benefit, they could always run his fortune into the ground himself. For instance, by buying lots of stock in companies that are about to go bankrupt. Whoever inherits will get a lot of worthless stock certificates.
State laws govern what happens if you die without a will or with a will ruled invalid.
In Hawaii, for instance, your spouse is guaranteed at least fifty-percent of your estate. The other half with be distributed among your children. Two children, then half of half or twenty-five each. One child, fifty. If you have no children, then this half is distributed among your parents, similarly. If you have no spouse or parents, your children get to divide it all among the. If you have no children or parents, your spouse gets 100%. If you have no children or spouse, your living parent/s get 100% divided among them. No parents, spouse or children, your siblings get to divide it all among themselves…