Fig. under control, as one would control a marionette. (*Typically: get someone ~; have someone ~; keep someone ~.) She keeps him on a string so he won't get involved with other women.
Under someone's control, as in She'll drop everything whenever Sam asks for something-he's got her on a string. This expression, alluding to pulling an animal on a leash, dates from the late 1500s, when it was put as in a string.