1) How long was your wife resident for?
2) Are you saying she lived in the US for 3+ years without green card?
3) Why didn't you apply for I-90 within a 90-120 days of not receiving the card? If it's USCIS fault, it would have been free.
4) How did wife come to the US? On K-1 / CR-1 or IR-1? Or did she adjust status in the US?
5) Did she need to file for I-751?
Too many questions, I know, but without it's hard to tell whether your wife is indeed a resident and whether she's eligible to apply for N-400.
In general, it's possible to apply without GC (again, if eligible, we need to establish all facts).