Mom dies. They each own half as tenants in common (so Bro’s share goes to his widow unless he directs otherwise). Then a dispute arises over paying expenses. So he deeds the remainder interest in his share to Sis. He keeps the life estate. What does she do with her half? Nothing? She still owns it, so basis still goes back to FMV at Mom’s death. As part of the agreement, did she assign him all the income from her half? Or has she just not been enforcing her rights to it, and therefore not reporting it on her returns?

Your situation is covered by one of these two examples, from the Iowa State University Center for Agricultural Law and Taxation:

If a decedent had an interest in a life estate at death, the property does not receive a step up in basis unless the life estate was a retained life estate granted by the decedent. In this case, the life estate property remains in the decedent’s gross estate.

Example: When Harry died, he had a life estate in a farm that was granted to him by his grandfather’s will. At his death the farm passes to Sherry, who held a remainder interest. After Harry’s death, Sherry’s basis in the farm will be the FMV of the farm at the time of Harry’s grandfather’s death. This is because the farm, in which he had a granted life estate during his life, was never part of Harry’s estate.

Example: When Harry died, he also had a life estate in a house. This life estate arose when he deeded the house, which he originally owned, to his children, retaining a life estate for himself. In this case, the basis in the hands of Harry’s children will be the FMV of the house on the date of Harry’s death. This is because the house, in which he had a retained life estate, is included in Harry’s estate.

https://www.calt.iastate.edu/article/gifting-selling-or-inheriting-question-basis 

But really, this isn’t a tax question. It’s the plot of an HBO miniseries.