Eligibility for Medicaid requires that recipient basically spend down all of their assets first (I believe you are allowed to keep a total of $10,000). There is also now a 5 year reach-back period, meaning that if the applicant has given any assets to others in the previous 5 years, those too must be used up before you are eligible. Also, Medicaid is not likely to cover many aspects of home care - I believe each state defines what they'll cover but typically, it's limited to those costs associated with medical care, such as physcian and nursing visits, testing, some equipment or pharmaceuticals, etc., not the ancillary costs of caring for someone at home. Ironically, Medicaid often covers most of the cost of nursing home care, which is usually far in excess of the costs associated with caring for a loved one at home.
Of course, almost no nursing homes will take Medicaid patients: Most LTC's - and certainly the better ones - will admit only pataients with significant amounts of assets that must be assigned to the facility. Once the assets have been exhausted (which happens rather quickly since the monthly charges can easily run to $12,000 or more), then the facility will accept Medicaid.
Great system, isn't it?