This is a conundrum brought about by abysmally low pay to nursing home caregivers, and by Medicaid reimbursement rates so low it is difficult for nursing homes to stay in the black. The majority of nursing home residents are covered by Medicaid.
If you want to greatly increase the odds you will not wind up in a nursing home, you need to own long-term care insurance (LTCi). Most LTCi policyholders are able to remain at home or move to an assisted living facility, instead of a nursing home. The evidence is in a recent AHIP study sited here; ask and I will email the complete study to you.