Regardless of what "this person's" drivers license says, were they a resident of NJ or PA? There are a number of factors that go into residency - most notably where you actually lived (and for how long, etc.) Assuming it is possible to fairly easily ascertain residency, that person, if a resident of Phila will owe city wage tax. It is not necessairly the company's absolute obligation to withhold Phila city wage tax. I have represented a few people who worked in NJ or NY while living in Phila who tried to claim they did not know about Phila wage tax and they all "lost" - in that they still had to pay the (properly calculated) tax. It was more a question of how much of the interest/ penalties the dept of revenue chose to abate. If the taxpayer took advice from HR that is on them - it is going to be the taxpayer's responsiblity to get competent advice about what taxes they owe, how they should withhold, etc. - this is why I think most people should use a CPA even if they think their situation is simple.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature.
Generally, a relationship between a taxpayer and a taxing authority is one based on law and the adage "ignorance of the law is no excuse." A Philadelphia resident - to the extent a taxpayer is a resident of Philadelphia - is generally required to pay taxes on his or her earned income wherever derived. Relying on an HR department's "advice" that a taxpayer misrepresent his or her residency is generally no excuse against tax liability. To wit: "keep your PERMANENT address in their system as NJ even though the driver's license/residency is Phila)." Moreover, a taxpayer cannot rely on the advice of a third-party that encourages tax evasion or unlawful tax avoidance. Generally, each taxpayer has an independent duty to correctly report to taxing authorities his or her correct residency no matter what a third party advises to the contrary. This can be verified through one's W-4 and pay stub deduction categories.
A taxpayer who does not pay taxes relying upon an non-authoritative source (like a large company's HR dept. as opposed to legal advice from an attorney or the taxing authority itself) is liable for any unpaid taxes. However, the taxing authority may be convinced to exercise discretion or leniency in a matter in which there is an honest - but legally inexcusable - mistake. Because the hypothetical implies that the HR department merely "said" to just keep the NJ address, the taxpayer is likely without any persuasive evidence to the effect that there was, in fact, an actual honest mistake. (E.g., he said/she said.)
Generally, if one cannot afford to pay a tax bill, the taxing authority may have a program that permits payments over time and/or even forgives or compromises in certain circumstances.
Disclaimer: Nothing stated herein is legal advice. For legal advice, consult an attorney; I am not your attorney at this time. This response may constitute ATTORNEY ADVERTISING which has not been approved by the Supreme Courts of New Jersey or Pennsylvania or the Court of Appeals of Maryland. I am a federally-designated “debt relief agency” that provides, where appropriate, relief under the U.S. Bankruptcy Code.