he entered the US.

It is possible that US homeland security might allow him to keep the GC if he could show certain evidence such as owning house in US, proof of NYU employment, or family members living in US. Also if he is still getting pay from NYU, he would have tax withdrawn and paid by the NYU payroll office.

Therefore, it is likely that he is still holding a valid GC and paying tax to IRS, but whether he pay enough, it is questionable.