Ohio runs several separate Medicaid HCBS programs rather than one combined waiver. PASSPORT and Ohio's Assisted Living Waiver are the two most relevant to a family comparing home care against a move to a licensed community.
PASSPORT: in-home services only
PASSPORT pays for personal care, homemaker services, adult day care, respite, home modifications and similar in-home supports for seniors who need a nursing-facility level of care but want to remain at home. It does not pay for assisted living room and board.
Ohio's Assisted Living Waiver: care services inside a licensed RCF
This is the waiver that actually pays for care services delivered inside a Residential Care Facility. It still does not cover room and board -- only the care component -- and not every RCF holds a provider agreement, so ask directly rather than assuming.
Applying
Both programs are administered locally, for our coverage area, through the Council on Aging of Southwestern Ohio, which can also tell you current waitlist status.