Generally, (and 'm talking at the federal level. I can't speak for state taxes and how states deal with estates) after all assets are transferred into the estate, it is the estate that pays any taxes due prior to distributing those assets to the named beneficiaries. With rental property, I'm not exactly sure how the depreciation recapture is dealt with. But I do know that at some point, that depreciation is recaptured and taxed. It's doesn't just "go away" with the passing of the deceased. I've not looked it up, but I would think the estate would recapture the depreciation and pay tax on it. Of course, I could be wrong on all this as I've never had the question asked on that specific matter before.
Your situation is significantly more complicated by the absence of a will, and the existence of "letters of promise". Kind of reminds me when Howard Hughes passed away back in the 70's. He was a multi-billionaire with no will, and the "letters of promise" started coming out of the word work once it was revealed there was no will. It took nearly a decade to get his estate settled.
So that's why you have to be careful here as the administrator of the estate. It's also why you need lawyer. All you need is to get this estate "settled" and then a few months later someone else produce a "letter of promise" to challenge that settlement. If I recall, what was done for the Howard Hughes case was a public notice of a "drop dead" date. In other words, a public notice was published in all the major newspapers stating that if anyone had any proof of Mr. Hughes leaving them something, they had until a certain date to produce that proof to the probate court. Then any proof submitted after that date, weather is was valid or not, would not be "entertained".
Sounds to me like this is something that needs to be done in your case. Of course, you don't need to advertise nationwide. The local paper where they lived the few years prior to their passing will suffice. But again, I'm not a lawyer and it's why I recommend you seek the services of a lawyer. (I may be incorrectly assuming you have not done so already. If so, my apologies.)
