All perfect praise be to Allah The Lord of the Worlds and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Islam has built marriage on love, mercy and understanding, and required spouses to fulfil rights and obligations. In case of having many wives, the man is obliged to spend on them and treat them justly. In fact, the husband is obliged to spend on the wife in all situations-save when she is defiantly disobedient-and provide her with a place of residence, even if she is rich.
There is scholarly consensus on the above where Imam al-Nawawi (May Allah have mercy on him) said, "According to the texts of Sharia and the consensus of the scholars, the husband is obliged to spend on his wife."{Rawdat At-Talibeen, V.9/P.40}. There is a famous rule amongst jurists which states that every person is obliged to spend from his/her wealth save the wife, since her husband is obliged to spend on her."
Al-Imam Al—Shirazi(May Allah have mercy on him) said, "If the wife choses to stay with her husband although he doesn`t spend on her, it is permissible that she forsakes him in bed."{Al-Mohathaab, V.3/P.155}.
In conclusion, if the husband abstains from spending on his wife, then she isn`t sinful if she forsakes him in bed. And Allah knows best.