Programming language where every expression makes sense
Redcode, the assembly language behind codewars, was explicitly written to have very few halting instructions, because the code often gets mangled before it finally gives out, and the more opportunities it has to halt, the less interesting the game is.

You see very few such languages in practice because we don't just want a program to run, we want it to run in the way we expect.  If you can make a typo and change the way the program ran, it must be acceptably close to the original expected behavior, or the programmers with seethe in frustration.

There is some precedence for such things by using natural languages rather than formal languages, but it's not what I would call a large field when you compare it to the use of formal languages.  If you're interested in such programming languages, the natural language processing community is where I'd look.

Another field you could look at is genetics.  There are remarkably few genetic sequences which are simply invalid.  Plenty of them that aren't very effective at reproductions, but very few invalid ones.