Laws vary by state. However, it is generally very difficult to get them placed. Some states have laws that forbid admittance to a nursing home by any felon.
TRg2020, your profile says you are homeless, so is it safe to assume you are on Medicaid? I would contact a social worker at your county's Dept of Health and Human Services and they may be able to either answer your question or direct you to someone who can. I can't imagine you would be rejected from a county Medicaid facility, but again -- don't make any assumptions. Or see if your county has any free legal services available to you. I wish you success in finding a place to land.
https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.americanconference.com/preventing-and-defending-long-term-care-litigation-803l14-mia/wp-content/uploads/sites/1391/2016/08/StateSurvey.pdf&ved=2ahUKEwiBksi_3p_pAhUjT98KHW4vA_0QFjAKegQIBBAB&usg=AOvVaw0B4ugOkS1tsRVBpLZ5jjUN