While there is probably a minimum for any given institution and you wouldn't be reduced below that for any reason, future salary increases depend most places on performance. There might also be a maximum. The limits might change from year to year, generally moving upwards for various reasons, such as inflation and cost of living. And there are wide differences between institutions and even between departments within a given university.
Chairs and/or deans usually have some discretion on awarding increases, but likely little in lowering salaries unless a person requests reduced duties also. This assumes there is no misbehavior, of course, which is more likely to result in dismissal than salary reduction.
I don't know, but suspect, that some laws affect the possibility of lowering salaries. In particular, there are some discrimination laws that might apply.
Most salaries are set on an annual basis and some grants might provide some additional funding for an individual. Salary may depend on an annual (or similar) evaluation or self evaluation.
However, at State Universities, the budget is influenced by political action. The budget for a department might be reduced, requiring difficult decisions to be made. But this isn't a performance issue, but a political one. Some departments are abandoned, though tenured faculty then are usually offered positions in other departments to the extent possible. And, at private universities, the budget may be dependent on outside factors that also require difficult decisions. But such things often involve faculty input in some way.
Moreover, I think that salary reductions, if known would be disruptive and a stain on an institution for other than misconduct or financial exigency. And both of those often result in hits to institution's reputation.