A pre-war parlor game featured little wooden figures that were moved around (as in a board game). The figures represented members of a typical family and were kept stored in a box. The idealized musume (daughter) came to symbolize the shy, sheltered character of a girl who has never left home (the box). Hakoiri musume refers to an unworldly daughter from a good family.
A: Kyooko-san, Amerika ni ryuugaku suru n desu tte.
B: Ara, sore, otoosan mo okaasan mo OK shita no? Anna hakoiri musume o Amerika ni dasu nante sazokashi shinpai deshoo nee.
A: I hear Kyoko is going to the States to study.
B: Oh? Did her parents approve? They must be very concerned about sending such an over-protected daughter off all the way to the States.