Have you have any experience in which a non-IT person works with a programmer during the coding process?

It's like pair programming, but one person is a non-IT person that knows a lot about the business, maybe a process engineer with math background who knows how things are calculated and can understand non-idiomatic, procedural code.

I've found that some procedural, domain-specific languages like PL/SQL are quite understandable by non-IT engineers. These person end up being co-authors of the code and guarantee the correctness of formulas, factors etc.

I've found this kind of pair programming quite productive, this kind of engineer user feel they are also "owners" and "authors" of the code and help minimize misunderstanding in the communication process. They even help design the test cases.

Is this practice common ? Does it have a name ? Have you had similar experiences ?