Is the funeral prayer offered for a devout woman who did not marry after the death of her first husband?

Yes, it is permissible to perform the funeral prayer for a deceased unmarried woman if she was known to be a Muslim. Her unmarried status does not prevent performing the prayer over her. However, a woman should not refrain from marriage if a suitable partner comes to her, unless there is a legitimate impediment other than devotional asceticism. This is because the Prophet (peace and blessings be upon him) commanded marriage and forbade celibacy, saying: "Whoever turns away from my Sunnah (definition) is not of me."