There's a thread over on the foreign professors in Korea Facebook group about blatant plagiarism on writing assignments. Some of the stuff is pretty shocking, but other attempts are definitely more subtle in nature.
Anyway, here's how I deal with it. I only have 2 "at-home" assignments, both worth 10% of the final grade, for a total of 20%. I give extremely specific topics for a very specific type of essay, word-counts and requirements for things like thesis statements and topic sentences. I guess some students could cheat on this, but it would be quite difficult. And even if they could, it's only 20% of their final grade so I'm not really worried about it. It would be impossible for a student to cheat their way to an A in my class.
The bulk of their grade (50%) consists of in-class exams that consist of actually writing an essay in 50 minutes. I give the students a list of about 25 possible topics and then a topic is randomly assigned to them depending on what desk they happen to sit at. I only allow paper or electronic dictionaries and not cell-phones, so it's impossible to upload sample essays or something like that.
It works for me, but I understand it's a pretty intense way to do exams in a writing class. The students don't love it, but I think that the better students actually appreciate the fairness of it and that the students who can actually write will get the higher grades, while those who are terrible can't bluff their way through it by getting a native speaker to write an essay for them, or something like that.