I failed the last semester in my program...and I wasn't alone. We started out with almost 200 in our class and just under 60 made it to the end. I was devastated to fail, being so close to the end. But our program was crazy - the last 2 semesters, we only had two tests: a midterm and a final. Imagine the sheer amount of information you had to be confident on, had to remember, for only 2 tests. You had no real chance to fight for your grade. The program's rational for so few tests was that they were "preparing" us for the state board, where we would only have one shot. Which made no sense, because being in school and learning is different than taking the NCLEX. But whatever. I went into the nursing program on the deans list, but graduated, finally, with a C. It was brutal, hardest thing I ever did. I aced the NCLEX, though. It was easy compared to school.
if you want to reapply, you just need to go to the school and tell them. I had to wait a year, and do the last semester with the class behind me. Luckily, because of all the students who failed in my class, they increased the number of tests.