It depends on the local culture. I've never heard of anyone setting absolute rules, but I could see it happening on the smaller levels such as a single district. Frankly, if the state tried to make a blanket law for all teachers to follow, they would have one heck of a fight on their hands. Most teachers I know, including myself, would view that as invasive micromanaging. Two examples that might help:
I went to High School "A" in a very nice neighborhood. Suburban, pretty affluent, extremely high test scores, that sort of thing. It was understood that the chance to re-do work was a privilege, and the teacher had every right to refuse such a request. Most of the time they let us do it, but not always. The only universal rule was that if you had an excused absence (for example, if you were sick), you had three days to collect all the work you had missed and turn it in. If you were unexcused (cutting class or something like that), you had no such right. That rule was set by the principal and only applied to our specific school.
I taught at High School "B" in a less nice neighborhood in the same city a few years later. Also technically considered suburban (we were the first neighborhood outside the urban core), though it felt like the inner city school I student taught at. The community was generationally poor and the schools were struggling to maintain accreditation. We had no set rules whatsoever. However, my students assumed that they automatically had the right to re-do work however many times they wanted, whenever they felt like it, and that I had to accept it for full credit no questions asked. When I refused on the basis that deadlines are important and there have to be consequences for one's choices, they made a HUGE fuss about it. Much to my surprise, the other teachers supported my students, arguing that "they did it eventually so it didn't really matter". It went all the way to my principal (unofficially; as far as the district was concerned, nothing was happening), who thankfully accepted my comparison to a teacher "eventually" writing lesson plans and gently chided us all about having higher standards before letting us go straight back to deciding for ourselves how it would work in our own classrooms.
I'll also say that in both high schools, some of it does boil down to relationships. Teachers do cut the "good" kids more slack. I had a teacher completely waive an assignment for me once - completely unheard of in my high school - just because I worked so hard in his class otherwise. And as a teacher, I often used the privilege to cut deals with my students. For example, be on time for the rest of the week to prove that you're serious, and I'll let you re-do assignments x, y, and z.