The hagwon industry is a very competitive one in Korea. Teaching English is a lucrative business which requires little effort and where profits can be high, but still a lot of hagwons fail.
If your hagwon didn't pay you, this is what might have happened:
There are big hagwons in Korea whose reputation is intact and who make record profits every year. Some dream of reaching such a level and open such hagwons.
Reputed hagwons have everything a decent hagwon needs: they are expensive, but their teachers have experience, they are very strict about what should be taught and how, that is, they delineate the curriculum very carefully and train teachers to teach efficiently. For example, they will tell their teachers that if a student asks a question, they provide a simple answer, and if the student is not satisfied with the answer, they just tell him that the question will be studied later.
However, a number of hagwons open without knowing anything about language teaching. All they think about is the money they will make teaching English. So they find a building, hire the first teacher who applies for the job, and don't provide teachers with teaching guidlines, and sometimes don't even give teachers textbooks.
Such hagwons practice low prices to attract as many students as possible. But they don't divide students by language ability or by level, they mix students using arbitrary criteria such as age, or sometimes don't have a policy on how classes should be divided at all. So teachers end up without textbooks, in classrooms where some students speak advanced English while others don't speak a word of English.
Teachers end up being clueless. They don't know what to teach or how to teach, and can not manage a class where students' levels are heterogeneous. Some focus on students with advanced knowledge of English and forget to take care of those who have more difficulties, while other teachers focus on students with difficulties. Also, rather than advancing steadily in curriculums that teachers often designed themselves, they tend to stop at one particular point of English grammar or one particular word, and may spend a whole class teaching that particular point.
A blunder that such hagwon managers make is that they don't take into account the fact that parents and adults in Korea often attend hagowns in order to get better tests at their scores. While experienced hagwons tell their foreign teachers how to focus on such tests and to teach what might come up in such tests, many hagwons do not tell their teachers to focus on students' tests. So angry parents and adults attending such hagwons find out that what is taught there is not related to the tests that they are taking.
Parents notice that their children are not making progress in class, adult students notice that they are not learning much from the class. Test scores do not improve for both students and adults. Such parents or adults often post negative reviews on Internet forums related to the hagwon, and the hagwon has difficulties attracting new students. Such hagwons often end up going out of business.
So, if your hagwon did not pay you or paid you late, it is a better idea to quit, because such hagwons are often in difficult financial situations and their reputation is so damaged that they can not attract new students.