For some countries and depending on the field, aside from scholarships which you can apply for, you can have your PhD sponsored by the department you're under. A Korea University graduate talks about this here. She was able to get around 25% sponsored, and she even receives stipends and she didn't really have to worry about her housing.
Granted, she does study in a non-English speaking country, but it could still help! I found it was interesting since it wasn't a very common way to pay for student expenses abroad.