do safety engineering schools exist?

Yes safety engineering schools exist! Schools in your area that are smaller are always safeties (in Ohio that would be like U of Akron, etc.) But there are plenty of larger school songs that have a little less competitive but excellent programs such as OSU and Cincinnati. I actually have a friend that goes to Ucinci for computer engineering and she absolutely loves it and is receiving a great education! And Ucinci is a safety school. So my advice would be to look at some of the smaller universities near you or some non-competitive engineering program large schools. Those would be your safeties.