However, if you are fired or "discontinued" or whatever term school districts use when they fire any teacher regardless of length of service, every single school district will ask the "weeding out" questions on the applications (have you ever resigned in lieu of a dismissal, failed to complete a contract, etc.). That is effectively blackballing teachers from careers in neighboring districts and often statewide. You will NOT make the cut even for an interview (unless, of course, you have some kind of connection with the new district).
In my previous state, there were at least six questions asking the same thing in order to weed teachers out on at least the applications of the two largest districts. These questions include if you have been denied tenure, if you failed to complete a contract, if you have ever been terminated. These effectively bar teachers from teaching in those districts; otherwise, the questions would NOT be asked.
After all, just because a district let you go for reasons having nothing to do with real misconduct doesn't mean you couldn't be a perfectly good teacher elsewhere. It's really none of any district's business if you have been non-renewed or fired.
Furthermore, many applications require you put down the name of your last principal. If that principal chooses to trash you on a reference check, you are dead in the water there.