I'm sorry to know you're needing to deal with (or anticipating needing to deal with) this.
I was not estranged from him, but my dad was mentally incompetent (dementia) when he died, and had been for years prior. He died after years in a nursing home, with no will and very limited assets and debts (basically, he had a checking account with under $2K in it, and income from social security he was obligated to pay to the nursing home and I had to deal with making sure the final bill to the nursing home got paid, plus a few costs associated with finalizing his "estate," i.e., documenting that everything got processed). Although I had had a power of attorney while he was alive, his death made that invalid, so I went through getting appointed as the administrator of his estate and getting everything taken care of. I also arranged his burial.
Laws vary state to state, but I don't believe you have any legal obligation to do anything. There should be (local government) officials in your state and your parents' (which is likely the relevant location) who can tell you.
If your parents die in a medical setting, I expect you'll hear from the medical officials, if otherwise, well, I don't know, but police seems possible. If you can, I'd make sure that you are listed as next-of-kin (assuming that you want to be contacted). But if you are, the dire warnings that get promulgated about people not being allowed to make medical decisions for others notwithstanding, my experience was the opposite, that even without documentation (of my right to do so), medical authorities wanted me to be the one who made medical decisions for my dad -- it was me or them (where I think this might have changed would have been if yet another family member had challenged my right to do so -- but no one did). So you may find yourself in that situation too, unless legal documents explicitly prevent you from doing so (not sure whether your use of the word estrangement reflects a legal situation or just reality).
Settling the estate of someone who doesn't have much isn't terribly complicated or expensive, though it can be annoying (keep paper documentation of everything down to the penny). Arranging a burial isn't, either. My dad hadn't wanted to be cremated (which would otherwise have been my choice) and I respected that and his other wishes and basically opted to spend some extra money to have a local funeral home take care of some of the arrangements, but mostly it was a matter of making some decisions and signing papers (and paying for what I'd chosen).