Nestled between the Mountains of Pelelelimara and the Forest of Hairy Trees sits the Village of Inexplicable Babies. In truth, it is perhaps more of a small town, home to nearly one thousand people, but there is relatively little infrastructure, and in appearance, it is more of a village than a town.
There are no roads or waterways passing through, and it is hard to imagine why the town exists here, but it does. Few pass through.
The Village of Inexplicable Babies has a single defining feature: the inexplicable babies. Anytime a person in the village, whether native-born or a foreigner, opens something large enough to hold a baby, there is a chance - admittedly a small one - that there will, in fact, be a baby inside. These children seemingly do not belong to anybody - they are simply there. The villagers view finding a baby as becoming a parent. Small children seemingly never find babies, only baby dolls.
In contrast to this, all of the natives of the village are barren - they receive children only by finding them. You might think this would lead to a culture where everything is always open except for perhaps one or two cupboards, and prospective parents just repeatedly open these until they get lucky, but it does not work is way - the villagers are seemingly happy with the randomness in their lives.
In any case, the villagers become very upset if visitors refuse to care for a child they find - they won't attack them (unless the baby is grossly mistreated), but they will shun them and refuse them any hospitality or assistance.
The Midwife Why is there a midwife in a village where no one is ever pregnant? Well, children happen very suddenly here. It's not like outside, where you may get nine months to prepare - here, one minute you have no children, and the next minute, you've got a squealing baby. The midwife runs a small school where she teaches people how to care for children. What will happen when she dies? Maybe she's looking for an apprentice.
The Cabinetmaker The cabinetmaker hates his job. He's constantly opening and shutting the things he's working on, and thus he has a lot of children. But it's a very lucrative position - everyone wants their baby to come out of a very fancy cabinet, and not some plain woodwork, and so he is paid well and gets lots of work. But he would sure love to find a way around his problem.
The Mayor The Mayor has some idea of turning the Village of Inexplicable Babies into a pilgrimage site. He's trying to lobby the Church of the Goddess to have it declared a holy site.
I Want a Baby
Some important figure (Queen, King, Whomever) is barren and eager for a child. The PCs may be employed to escort them here, and then back again with their small child, through all sorts of danger, no doubt.
I Don't Want a Baby
Someone, a PC or perhaps someone traveling with them, passes through, not knowing about the village, and ends up with a totally unexpected baby. What to do with it? If the village is not widely known about, this could be very embarrassing for a married or chaste character.
Tarzans of the Apes
Long after the village is in ruins, a group of apes ends up raising a bunch of Inexplicable Babies.
Some incredibly horrible group of people or demons or something has decided that an endless supply of babies would be perfect for eating or sacrificing.
Instead of a village, it could be a convent or monastery or group of amazons or... whatever the male equivalent would be. No need for kidnapping or trysting or recruiting, you've got children from heaven. Or from your kitchen, technically.
Where Are All of These Babies Coming From?
Who knows? They're inexplicable! But some plausible explanations:
The village was blessed by a fertility or chastity god.
The village was cursed by a witch or sorcerer.
On a distant planet, horrible alien intelligences are transporting their minds into babies to infiltrate the earth.
Before Gallifrey blew up, the Time Lords put all of their babies in TARDIS cupboards and inexplicably sent them here.
They are the long-misplaced babies of an ancient civilization, one which collapsed when it accidentally misplaced all of its babies.
They're actually clones. Some sort of magic turns things into cloning vats inside the village.
Somebody made a very poorly worded wish at some point.
Please feel free to offer your own explanations.