The third Cinderella tale type in Cinderella Tales From Around the World is ATU 510B* The Princess in the Chest. This is by far the smallest subset but still stands out enough to earn its own tale type. The tale is closely related to 510B since many of those have the heroine hiding in a wooden dress à la Donkeyskin to escape her father's marital machinations, especially many Italian variants. Uusally the big difference between this version with the chest and the wooden dresses is that the father disposes of the chest himself, selling it when he cannot find his daughter, usually on their planned wedding day. The dress, however, becomes a disguise.
Hiding in chests is fairly common in fairy tales--this device is also used in some Bluebeard variants, for example, to escape the murderous husband.
From my intro to the book:
ATU 510B* The Princess in the Chest
This tale in the Cinderella Cycle is the least common but still bears enough differences to receive its own classification. One of the earliest and best known versions can be found in Straparola’s Piacevoli notti (The Facetious Nights) circa 1550 and is commonly known as Doralice.
A king decides to marry his daughter and she requests a chest as one of her conditions for marrying him. She hides in the chest, virtually disappearing on her wedding day. Her father sells the chest and a prince from another realm acquires it. The prince stores the chest in his room where the princess emerges secretly to eat his food and perform other tasks while he is away. He discovers her and falls in love with her, keeping her presence a secret until his family finds her and sends her away. He falls sick upon her absence and receives food prepared by her hand with one of his rings hidden inside. He finds her by indentifying the ring—or other object—and marries her.
The present book’s organization does not break out this small subset of ATU 510B* The Princess in the Chest into its own section, but includes the few tales of this type in the larger ATU 510B section.