Women of all levels of society contributed financially to these communities. Those who contributed on a smaller scale could be sure at the very least that this would gain them some spiritual benefit. On a more practical level, a woman who attached herself to a monastery by making such donations would have an easier time joining the community later. Some women actually exchanged their property for lifelong support. An older single woman (whether unmarried or widowed) with a modest amount of property might give it all to the monastery with the caveat that they provide for her for the rest of her life.
Wealthier women often gave much larger donations, receiving correspondingly larger benefits in return. Many founders stipulated* that they be buried in the church there and that particular services be said for their souls and for those of their family members. Their relatives often got preferential treatment should they chose to join the community. Some reserved the right to appoint the community’s superior. A wealthy donor could also have services said for her soul, and of course, no matter the size of the donation, this very act of charity was considered a pious benefit.
Many monasteries (both male and female) also had an official protector. Some founders desired a male protector for their nuns, others felt a female protector was more suitable.** This person was responsible for the physical and political wellbeing of the community. They acted as a liaison between the nuns and the outside world, seeing that the community had the resources it needed, making arrangements for building repair, and heading off any political threats.
Very few women ever became monastic protectors. Many, however, contributed financially to the benefit of themselves and the communities they gave to. They did so for several reasons ranging from the pious to the practical, usually a mix of them.
*The sources we have for this are the typika, the foundation documents for Byzantine monasteries. Similar to a monastic “Rule” in the western Church.
**For example, the protector of the monasteries of Kecharitomene (early 12th century) had to be a female relative of the founder, Irene Doukaina Komnene, while the founders of Lips (late 13th century) and Bebaia Elpis (early 14th century) felt that a male protector would be more suitable. While in some cases a woman could officially be the protector of a male community, it was expected that her husband or son would actually do the job.
Thomas, John and Angela Constantinides Hero, eds. Byzantine Monastic Foundation Documents: A Complete Translation of the Surviving Founders' Typika and Testaments. Washington, DC: Dumbarton Oaks, 2000. [Text may be found here.]
Chapter Three, "The Protectorate" - Dumbarton Oaks
Empress Irene Doukaina, Typikon of Kecharitomene, 1110-1116, translated by Robert Jordan - Dumbarton Oaks
Theodora Palaiologina, Typikon of Lips, 1294-1301, translated by Alice-Mary Talbot - Dumbarton Oaks
Theodora Synadene, Typikon of Bebaia Elpis, 1327-1335, translated by Alice-Mary Talbot - Dumbarton Oaks
Talbot, Alice-Mary. "The Devotional Life of Laywomen." In Byzantine Christianity, edited by Derek Krueger, 201-220. Minneapolis: Augsburg Fortress, 2006.