Is it wrong to manipulate your finances to qualify for welfare?

An acquaintance of mine -- who is moderately wealthy -- feels justified in manipulating her finances to get government aid whenever possible on the grounds that it is "getting back" some of what she has paid. For example, she had her elderly mother buy a new car for her own use, in order to have her mother deplete her savings faster and qualify for Medicaid. However, while she had paid much in tax, her mother collects more in social security every month than she ever paid in taxes. Is it rational to view this as "getting back" money that was taken inappropriately, or is it actually immoral and self-destructive?