"비에 옷이 젖었습니다."
Translation:My clothes got wet in the rain.
It's contextual. The subject is often dropped in Korean sentences because 9 times out of 10 it's obvious who you are talking about.
In the above example, if you came home soaking wet and told your spouse "clothes got wet in the rain", it'd be pretty obvious you were talking about your own clothes.
On a side note, because there are no actual context clues for us in this sentence, any subject should be allowed in the translation, not just "my".