The rationale, which you can trace back as far as ancient Roman law, is that children have a duty to care for parents. The law sees this as a matter of ethics and reciprocity: Your parents took care of you as children; now it’s your turn to take care of them.
At one time, filial responsibility laws were far more common. As recently as the 1950s, 45 states and the federal government had them on the books. They began to erode during the New Deal, when the Social Security Act passed and the concept of government rather than familial responsibility started to take hold.
But 28 states still have filial responsibility laws: Alaska, Arkansas, California, Connecticut, Delaware, Georgia, Idaho, Indiana, Kentucky, Louisiana, Maryland, Massachusetts, Mississippi, Montana, Nevada, New Hampshire, North Carolina, North Dakota, Ohio, Oregon, Pennsylvania, Rhode Island, South Dakota, Tennessee, Utah, Vermont, Virginia and West Virginia.
Sixteen of these impose civil penalties — they can come after your assets or income if you fail to support your parents. In the eight states where filial responsibility entails criminal penalties, a prosecutor could actually put you in jail. Four states take both approaches.
In Massachusetts, for instance, someone who “unreasonably neglects” to support a parent who is destitute or too infirm to maintain himself could face up to a year in prison plus a $200 fine.
So it’s no urban legend — a state could come after grown children who fail to support their parents. But it seems an unlikely prospect. To ascertain the law in your state and how it has been used, I strongly recommend consulting with a local elder law attorney.