If a person who had a daughter but no sons passed away, may the daughter recite Kaddish for her deceased parent?
The Shebut Yaakob (Rav Yaakob Reischer, 1661-1733) ruled that a daughter may recite Kaddish for a parent if ten men assembled in her home, but not in the synagogue. Likewise, the Teshuba Me'ahaba (Rav Elazar Fleckeles, 1754-1826) writes that this was done in Amsterdam, with the approval of the local Rabbis. He adds that it was customary in Prague for elderly men and women to sit in the Ezrat Nashim (women's section) of the synagogue and recite Tehillim all morning, and if there was a girl whose parent had passed away without sons, the daughter would recite Kaddish after the Tehillim reading. This was done in the Ezrat Nashim, but not in the main section of the synagogue.
The Teshuba Me'ahaba explained that women are no less obligated in the Misva of honoring parents than men, and so they should have the opportunity to benefit the soul of their departed parent through the recitation of Kaddish. Although this should not be done in the public setting of the synagogue, it is permissible if a private Minyan is formed. Hacham Ovadia Yosef concurred with this ruling.
A solution in such a case is for the family to appoint a man to recite Kaddish for the deceased. Rav Yosef Kolon (France, 15th century) ruled that one may recite Kaddish for somebody who was not a relative. He adds, based on an earlier source, that one may recite Kaddish for the souls of several different people, and so even if somebody is already reciting Kaddish for a parent, he may be asked to recite Kaddish also for a person who left the world without sons. Similarly, the Elya Rabba (Rav Eliyahu Spira, Prague, 1660-1712) writes that if somebody needs to travel during the year of mourning, and will be unable to recite Kaddish for a period of time, he should hire somebody to recite Kaddish on his behalf during that period.
It should be noted that there was a custom that the Rabbi would recite the final Kaddish – the Kaddish before Alenu – for the benefit of all those who had passed away without sons. Although this is not our custom, it demonstrates that when there are no men to recite Kaddish, this can be assigned to somebody else, even a person who is not related to the deceased.
Summary: If a person passed away without sons, and the daughter wishes to recite Kaddish for the parent, she may if a private Minyan is assembled in her home. The preferred solution, however, is for the family to appoint somebody – even someone who is not related to the deceased – to recite Kaddish for the deceased. This may be done even by someone who is already reciting Kaddish for his own parent.