Kyoshi's parents suspected that she was the Avatar
They would have known that Kuruk died around the time she was born, and as she was growing up she might have shown some signs of being able to bend water and fire as well as earth or air. They likely also would have known about the Earth Kingdom method of finding the new Avatar, and as Kyoshi grew older and the Avatar failed to be discovered, Jesa and Hark might have put two and two together and realised their nomadic lifestyle was preventing her from being found. Not willing to keep her from her destiny, they made arrangements for her to have a stable home so that the geomantric rituals could finally find her — and with nothing to keep them on the straight and narrow, they returned to their criminal life. And if Kyoshi wasn't the Avatar, Jesa left her the fans she used for airbending and her journal, so that they had a chance of meeting again. Kyoshi's daughter Koko was abandoned by her biological parents, just like Kyoshi
Avatar Extras for "The Warriors of Kyoshi" confirms Kyoshi had a daughter named Koko, and considering her relationship with Rangi, it seems likely that Koko was adopted rather than being Kyoshi's biological daughter. Kyoshi discovered a child abandoned by her parents and, not wanting the child to live on the streets begging for food like she once did, adopted her.