Succubuns are incredibly unsuited to parenthood, and Burrowgatory is no place for children. Fortunately, the demon Murmur is more than happy to take the burden of childrearing off their hands.
Family
Succubun culture doesn't have a proper concept of "family." They understand blood relations, but due to the fact that parents are rarely together for the long term and do not raise their own children, they do not attach any sort of relationship or emotional weight to the concepts of "mother," "father," or "sibling," etc.
As children, Murmur (or whichever demon raised them) is the only parental figure succubuns have. After returning to Burrowgatory, it's fairly common for new adults to be taken under the wings of older succubuns, who give them guidance or even teach them their trade. These arrangements can result in surrogate parent-child relationships, mentor-mentee relationships, or master-apprentice relationships.
The closest thing most succubuns have to familial ties are "littermates." Littermates are inseperable friends who were raised alongside each other, who remain very close even after returning to Burrowgatory—a relationship that lies somewhere in between the importance of childhood friends and siblings for humans. It's possible for littermates to be biological siblings, but more often, they're unrelated by blood. Like any childhood friends, it is not taboo for nonrelated littermates to become romantically or sexually involved.
Lineage
Succubuns are able to tell when they're related to one another by smell. They find the pheromones of blood relations undesirable and even somewhat unpleasant up close, preventing accidental inbreeding. Due to both biological and societal factors, succubuns are generally very uninterested in spending time with their blood relatives.
Succubuns do not track their lineages. Though the smell of a blood relation is stronger the more closely related they are, they have no way of telling what the exact nature of their relation is. It's possible for parent succubuns to recognize the coat patterns of their children, or for siblings raised during the same year to be able to tell that they're siblings, but otherwise, they can only guess as to the exact nature of their relations—not that they're likely to care.
Succubuns who want to leave a legacy will typically select a promising protegé from among the new adults returning to Burrowgatory, rather than entrusting it to one of their own children. Wealth and privilege are generally passed along through connections, rather than bloodlines.
Breeding
Succubuns aren't fertile the majority of the time, but are capable of reproducing once a year. Most succubuns go into "heat" for the duration of February, during which time they have a much stronger sex drive than usual. The midpoint of this season is a holiday known as Matentines, thought to derive from "mating times."
Due to their ability to alter their sexual characteristics, any two succubuns are capable of reproducing with one another. As succubuns do not become physically elderly, they can continue to have children for their whole lives if they wish.
Succubuns who get pregnant revert to their bun form and become unable to shapeshift for the duration of the pregnancy, for the safety of their babies. These pregnancies last for one month, and are not particularly taxing on the body. Succubuns typically give birth to only one or two children at a time, but it's not uncommon to see litters of three.
The Church of Sulfur provides a wide range of support for Burrowgatory throughout the duration of breeding season. To assure everyone is able to have experience they want, the church supplies medication to suppress heat, birth control, fertility supplements, and abortive care, as well as extensive care for pregnant succubuns. Throughout March, newly born babies are turned over to the Bunnery, where they're taken care of until the last of the season's baby buns have been born.
At the end of March, the Church of Sulfur delivers all of the newborns to Murmur, who will raise them or entrust them to other demons to raise. At this time, all of the succubuns born the previous year are returned to Burrowgatory as young adults, ready to find their place in the world.