Not necessarily. We can say that it is a vicious cycle, escaping from it is not that easy. But once you get your way out, there are a lot of opportunities to grab out there to get a good quality education. All that it needs is will and courage.
Government has come up with a lot of programs, under which poor children are given education free or at very low cost. The problem lies in the awareness at the end of the public, and execution at the end of the authorities. We all are familiar the conditions of government school due to which no parent (no matter how poor he/she is) would want his/her child to study in such school.
Those who tolerate studying in ill conditions and are very bright get very good opportunities in the form of scholarships during their higher studies. But unfortunately, the percentage of such students is very low. Most of the students think that it’s better to drop out and start earning money from the very young age. That’s when they enter the vicious cycle in which even their children would be caught.
So, the answer to your question would be that not all poor people are subjected to poor education, but a large number of them, unfortunately, is.