That is how it works in Minnesota. My mother in law exhausted her assets in just over one year, and Medicaid picked up the last several months. My Mom, whose house when sold yielded a decent sized Annuity policy, and whose retirement income was more, managed 5 years of self pay for increasing levels of care. We used Medicaid for about one year, and she had enough in her checking account at the end to pay for a catered funeral lunch (one of her final requests)
We ( 2 daughters and to a lesser extent 3 sons and several of her 18 grandkids) were heavily involved in her care up to the end, in spite of career and family obligations. It's what we were taught throughout our lives.

Also, I split my year between 2 communities with large immigrant populations. Multi generation and multi family households are still the norm. I feel sad for those who don't have these resources.
My kids have already shown they are ready and willing to step up, as have several nephews. So though we are preparing to pay as we go, family plans to be in the wings to oversee and assist.