Answer:
(Fatwa: 184/171=B)
Yes, in the abovementioned case you are not liable for giving nafqa (maintenance) to your wife (who, as per your question left home without your permission, and she does not do any work and earns herself): لا نفقۃ لخارجۃ من بیتھا بغیر حق و ھی ناشزۃ (در مختار)Basically, the maintenance from a husband is a compensation as wife stays at his home, now when the wife is away from husband on her own will then there is no maintenance on the husband.
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband
