Advice as above. Not replacing the card means you gave no way of demonstrating legal presence if needed ... it may take up to 15 months to go through naturalisation so you need to make the decision based on your individual situation. My opinion only .. I would risk being unable to demonstrate my LPR status if I had to.
If it’s a 10 year card, then yes, she can file for naturalization (I suggest the 5 year rule) without needing to renew her card. Do note however without a valid card, she cannot easily travel internationally. Also, if her employment changes, getting a new job will be difficult. N400s can take a Year to process.
Expiry of a 10 year card does not mean expiry of residence status, just the document expires. USCIS is very adamant in pushing that LPRs should have valid LPR cards, as with an expired one, you cannot immediately easily prove your legal status. It’s a risk you can take, but I don’t suggest it, especially since N400s take a long time. It is also law that she must carry a valid LPR card at all times.
