no you can't, plain and simple. it refers to the modal verb. I have to study. you can't omit the "to" there, and you can't omit it when changing the order around.

"To have (something)" and "to have to (do)" are different. "To have to (do)" is equivalent to "must (do)." He won't study, unless he must study. He won't study, unless he must [study]. He won't study, unless he has to study. He won't study, unless he has to [study].

Why do you have to include the word “to” at the end of your example. It’s simple. Because you have TO. That’s the way it is in the English language. Don’t ask why, just do it, memorize it. If you omit the word “to” it makes no sense to the sentence.

He won't study unless he has some diner. He won't study unless he has been to play first. He won't study unless he has been beaten He won't study unless he has to study. He won't study unless he has to. - without "to" we sit there wondering what follows. . Why? That's the convention for English. Unless he has to, he won't study. Unless he has to study, he won't study.