If she dies while being known to be a Muslim woman, Muslims have to perform the Funeral Prayer for her. Being unmarried is not a reason for not offering the Funeral Prayer for her. Moreover, a woman whose husband dies should not abstain from marriage if a competent person offers to marry her unless there is an obstacle other than worship that impedes her from marriage. The Prophet (peace be upon him) ordered marriage and prohibited celibacy. He said:
So whoever turns away from my Sunnah does not belong to me.
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.