You actually shouldn't do this!

This doesn't introduce a new scope, so accidentally using x outside of the case block is UB. Instead you should introduce a new scope like so:

switch (foo)  {
  case BAZ: {
    int x = ...;
    foobar(x);
  }
}

Can confirm

What does assigning ... do in C? Is that just default type value or something?

question, why is a declaration not a statement?

wonders of C

int x = ...; isn't just a declaration. Both are totally fine in most modern languages.

Can confirm. I have to do this all the time. Some coworkers just delete it, and I have to explain the situation every time when they see in the git blame that I put that semicolon there.

As someone pointed out in another comment, in switch statements you should just start a new scope with {}. But in actual labels it's just better to put a load-bearing semicolon. You don't need to put it in another line though, I just put them like this:

int main() {
    int *a = malloc(sizeof(*a));
    if (init_a(a) <= 0) {
        goto err;
    }
    do_something(a);
err:;
    int ret = 0;
    if (a == NULL) {
        ret = -1;
    }
    free(a);
    return ret;
}