What is the best way to bring up the topic of assisted living to and for the elderly person living in my home?

This article might help, it closes with researching and "tactfully" presenting the facts about the progression of illness. It's obviously an emotional conversation, but the fact is there comes a time when the best thing a person can do is acknowledge they can no longer provide the level of care someone needs.
https://www.agingcare.com/articles/how-to-talk-to-parents-about-assisted-living-153013.htm