In the olden times, a woman would need parental consent to get married, or worse, her groom would be chosen by her father. As a consequence of such element of culture, she would sometimes run away from home either to avoid an arranged or forced marriage or to marry a man her parents disapproved of. Is there a single word, a phrase or an idiom to define this action?
A woman might be said to abscond in such a situation (whether or not she went on to marry someone her parents disapproved of):
1 Leave hurriedly and secretly, typically to avoid detection of or arrest for an unlawful action such as theft:
If she ran away to marry someone other than the person her parents wanted her to marry, she could be described as having eloped:
Run away secretly in order to get married, especially without parental consent
(Definitions from Oxforddictionaries.com)