Does an expiation become obligatory for a sister who swore not to interfere in her sister's affairs and then broke her oath, and is it permissible for the sister to offer the expiation on her behalf secretly?

If the oath was unintentional, it is considered a laghw al-yamin (a vain oath), and no expiation is required for it. However, if she intended to swear the oath, then expiation is required: feeding ten needy persons, or clothing them, or emancipating a slave. If she is unable to do so, she must fast for three days. It is not permissible to offer the expiation on her behalf without her knowledge, as intention is a prerequisite.