Actually, PA has a "filial responsibility law" and this can indeed make a parent liable for necessary debts of an indigent child and makes a child liable for debts of a parent. Pursuant to 23 Pa.C.S.A. § 4603:
(a) Liability. --
(1) Except as set forth in paragraph (2), all of the following
individuals have the responsibility to care for and maintain or
financially assist an indigent person, regardless of whether the
indigent person is a public charge:
(i) The spouse of the indigent person.
(ii) A child of the indigent person.
(iii) A parent of the indigent person.
(2) Paragraph (1) does not apply in any of the following cases:
(i) If an individual does not have sufficient financial ability
to support the indigent person.
(ii) A child shall not be liable for the support of a parent
who abandoned the child and persisted in the
abandonment for a period of ten years during the child's
minority.

Under Section 1 (iii) it does say a parent of an indigent person can be liable unless according to Section 2) you do not have sufficient financial ability to support the indigent person.

This law is most frequently used to make children liable for the medical care of their parents, but as you read the text of the law above it can be possible for the law to make the parent liable for the care of an indigent child. However, your son has to be proven indigent to hold you liable. See Also: Healthcare Retirement Corp. of America v. Pittas 2012 PA Super 96 (2012).

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