There is a variety of legal methods that can be used to prevent an elderly couple's entire net worth from being consumed by nursing home expenses.
First of all, Medicare does not pay for nursing home expenses. It covers things like doctor visits, drugs, and a certain amount of hospitalization. Medicare is a "status-based" benefit, which means that all your parents have to do qualify is turn 65. It makes no difference how much they have in terms of income and assets. As each of them turns 65, that person qualifies for Medicare.
Medicaid, on the other hand, is a "means-based" benefit, which means you have to qualify for it based on how much you have in the way of income and assets. Although Medicaid is mostly funded by the Federal government, the States, who administer the program, are given a certain amount of leeway in setting the income and asset caps. Different States also interpret and apply some of the other rules differently from each other, so it is important for you to seek State-specific advice. The best we can offer here is general information.
The Federal guidelines set ranges of allowable income and asset caps, the most liberal being that a couple (where only one spouse needs nursing home care) may keep a total of $2,789 in monthly income, and they may own a house (having no more than $750,000 of equity), a car, household furnishings, a funeral plan, life insurance with a cash value of no more than $1,500, and $111,560 worth of other assets. Note that these numbers are all maximums. Many States are not this generous.
If the couple exceeds the Medicaid income cap, they are not necessarily disqualified from receiving Medicaid benefits. Their "excess" income must be used to pay nursing home expenses, and Medicaid can kick in on nursing home expenses that are over and above the "excess" income amount.
If the couple's holdings exceed the asset limit, they are disqualified from receiving Medicaid benefits. Accordingly, many of the acceptable Medicaid planning strategies involve "converting" nonexempt assets into exempt assets. For example, if a couple lives in a State that allows the maximum asset amounts listed above, but has $200,000 worth of "other" assets, they will not qualify for Medicaid. However, if their home has an equity of only $400,000, and if the "other" assets consist of cash, the couple can invest $88,440 ($200,000 minus $111,560) in such things as home improvements and furnishings, funeral plans, and a car, in order to bring their holdings within the asset cap.
Other legal strategies may be available as well. In order to get a definitive answer in your jurisdiction, you need to consult a Medicaid expert in your State. One excellent way to locate these kinds of resources is through http://www.eldercarematters.com/statechapters.htm, where you may find a listing of advisors in your locale. You can also find Hawaii-specific information at www.est8planning.com.