Short answer: Partly, at most. STAR+PLUS HCBS can pay for assisted living services for a person who qualifies, but federal waiver rules generally do not pay for room and board, so the resident still pays rent and meals from their own income.
Assisted living is not nursing facility care. Texas nursing home Medicaid pays a Medicaid-certified nursing facility; it does not pay an assisted living facility’s bill.
The route for assisted living is STAR+PLUS Home and Community Based Services, which lists assisted living among its services. The person must meet Medicaid financial rules and need a nursing-facility level of care.
Even then, federal rules for home and community-based services exclude room and board (with narrow exceptions such as respite in a facility). Medicaid pays for the care services; the resident pays the housing and meals. HHSC’s chart sets the personal needs allowance in assisted living at $85 per month for the co-payment budget.
Do not assume a Medicare Savings Program card or Medicare covers any of it; neither pays for assisted living.