Alyce and Runt have quite a lot in common. For one thing, they both have no family. Alyce was abandoned by her family, whereas poor little Runt is an orphan. Nowadays, we have social services departments and adoption agencies. But in medieval England, children without families were often on their own. Without a family support network and without money, they were in a dire situation indeed.
Because he's an orphan and no one wants him, Runt has been forced to wander from place to place, looking for food, warmth, and shelter wherever he can find it. When Alyce meets him for the first time, he's sleeping in a cowshed, which is probably the only place he can find to rest his weary head.
Alyce is in the exact same boat as Runt when she first arrives in the village. She has no one, no money, and no prospects. Skinny and pale, she's as poor as an entire cathedral of church mice. Like Runt, she's had to endure a string of hardships that most adults would find difficult to handle, never mind the fact that she is a child. And like the little orphan she finds asleep in the cowshed, her short life has been characterized by poverty, abuse, and hunger.
Under the circumstances, it's not too difficult to see why Alyce should be compelled to help Runt after she discovers him. Instead of driving him away, she shows kindness and consideration towards him, giving him some parsnip tops and cheese for his breakfast.