Tax withholdings gone to collections - whose fault?

Location: Philadelphia, and then a small suburb outside Philly.

TLDR: my MIL did not have the proper tax withheld from her paycheck for the last 1.5 years following remote work and moving her home. Her taxes have now gone to collections. I am trying to help her fix this. I believe her company should have helped her know what withholdings were required but they are telling me it was not their responsibility.

My MIL works for a company in Philadelphia and was living in Philly for the longest time. During covid, all employees became remote. When companies started to RTO, employees were given the option to come back full time, work hybrid at a small salary decrease, or stay remote at a larger salary decrease. My MIL opted for 100% remote and her salary decreased by approximately $10,000 annually. Her taxes were not adjusted at that time to reflect remote work (it wouldn't have mattered; she still lived in the city so she'd owe the same city wage tax whether the money was made at her home or her office).

Shortly thereafter, she moved out of Philly to a small suburb in PA, still working for the Philly company 100% remotely. She submitted a change of address form to her HR team but did not know or realize she would need to make any other changes such taxes. As such, her tax withholdings were not adjusted to reflect her new home location and remote employment outside of the city. She paid (and has been paying for 1.5 years) a premium wage tax to the city which would have been eliminated as she is no longer a Philly resident nor an employee working IN the city.

MIL's employer says MIL can request a refund from the city, but I do not believe we can do this without an amended W-2 properly reflecting the locality in which she earned her wages (her old W-2s state her locality was Philly even though her address on the W-2 is her proper PA suburb location). Otherwise it's just my word vs. the City of Philadelphia telling them "she was working remotely, I swear, please give her back the EIT she paid."

Next problem: when MIL moved to the PA suburb, she was supposed to start paying EIT to the new borough she moved to and no tax withholding updates were made, so she hasn't paid this for the last 1.5 years. She just received a notice from a collections agency that her 2023 EIT for that borough have gone to collections (which will occur again for 2024 and 2025 if I don't fix this). This collections notice comes with almost $100 of fees and penalties plus the $800 tax bill she owes.

I do not feel that my MIL is required to have the tax knowledge to understand when tax withholdings should change and feel it was her employer's responsibility to notify her that a change was necessary after she moved out of Philly.

They obviously disagree with me and say it's MIL's own fault that she didn't pay taxes to the right locality via her paycheck. All I'm asking is that they pay the <$100 penalties for the overdue taxes which they should have known she would have to pay. I'm not asking them to do the work to recover the Philly EIT that was incorrectly paid (although it's my personal opinion they should help with that too).

I don't understand why MILs HR department thinks employees should also be tax experts. Obviously they can't just change your tax withholdings on their own but why didn't they recognize a situation that might require tax adjustments, bring it up to her, and ask her if she wanted to begin withholding the proper taxes? Am I totally off base here in my thinking?