Praise be to Allah.
Yes, if she dies and she was known among the Muslims as being a Muslim, then the Muslims should offer the janaazah (funeral) prayer for her. The fact that she was not married is not a reason for not praying for her. But a woman whose husband dies should not refuse to get married if someone who is compatible and suitable comes to marry her, unless she has a reason – other than being devoted to worship – not to get married, because the Prophet (peace and blessings of Allaah be upon him) enjoined marriage and forbade celibacy. And he said: “Whoever rejects my Sunnah does not belong to me.”
And Allaah is the Source of strength. May Allaah bless our Prophet Muhammad and his family and companions, and grant them peace.