It first of all depends on what the laws of the specific state say. For example, Ohio is a state said to have such a law, but that law, ORC 2919.21 is more generally about the crime of non-support. So in fact,
(A) No person shall abandon, or fail to provide adequate support
to:...(3) The person's aged or infirm parent or adoptive parent, who
from lack of ability and means is unable to provide adequately for the
parent's own support
Divisions B and C of the statute are limited to court-ordered support and support of juveniles. The law then says that
whoever violates division (A) or (B) of this section is guilty of
nonsupport of dependents, a misdemeanor of the first degree.
Nothing in the statutory language limits criminal liability in case a person was not aware of a financial need of one of their parents. This legal brief by the Ohio Legislative Service Commission indicates (based on case law in Ohio) that
Outside the criminal law, an adult child has no legal duty to support
a parent unless a contract, express or implied, exists.
California has a law imposing a similar financial responsibility on children, and also has a law denying such responsibility. The "denying responsibility" part says
No relative shall be held legally liable to support or to contribute
to the support of any applicant for or recipient of aid under this
chapter. No relative shall be held liable to defray in whole or in
part the cost of any medical care or hospital care or other service
rendered to the recipient pursuant to any provision of this code if he
is an applicant for or a recipient of aid under this chapter at the
time such medical care or hospital care or other service is rendered.
This is about public assistance for the aged, blind and disabled. And moroever (and explicitly mentioning the other law),
no demand shall be made upon any relative to support or contribute
toward the support of any applicant for or recipient of aid under this
chapter. No county or city and county or officer or employee thereof
shall threaten any such relative with any legal action against him by
or in behalf of the county or city and county or with any penalty
whatsoever.
But still, under Family Code 4400,
Except as otherwise provided by law, an adult child shall, to the
extent of the adult child’s ability, support a parent who is in need
and unable to self-maintain by work
and under §4403,
(a) Subject to subdivision (b):
(1) A parent, or the county on behalf of the parent, may bring an
action against the child to enforce the duty of support under this
part.
(2) If the county furnishes support to a parent, the county has the
same right as the parent to whom the support was furnished to secure
reimbursement and obtain continuing support.
(b) The right of the county to proceed on behalf of the parent or to
obtain reimbursement is subject to any limitation otherwise imposed by
the law of this state.
(c) The court may order the child to pay the county reasonable
attorney’s fees and court costs in a proceeding by the county under
this section.
So in California, it's not entirely clear what the actual legal obligation of a child is.
You can make a successful claim against a child in Pennsylvania, see Health Care & Ret. Corp. of Am. v. Pittas (Pettas). And it turns out that you can sue across state lines, see Melmark v. Schutt (this case involves suing parents of a mentally disabled adult child), a variant but under this same filial support law). The parents, in New Jersey, were sued under Pennsylvania law (where the child was). However, this isn't a trivial matter, since it involves the complex subject of "choice of law". In this case, the court (PA Supreme Court) concluded that Pennsylvania had the greater interest in applying its law, thus the parents were held to the other state's laws.
