Is there a word or phrase for "running away from home to avoid an arranged marriage"
Solution 1:
A woman might be said to abscond in such a situation (whether or not she went on to marry someone her parents disapproved of):
VERB
[NO OBJECT]
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:
VERB
[NO OBJECT]
Run away secretly in order to get married, especially without parental consent
(Definitions from Oxforddictionaries.com)