override theme function in facetapi module
You're nearly there, but a preprocess function doesn't look applicable to what you're trying to do. A preprocess function is used to set up variables for a theme function, not to actually produce the markup. 

What it looks like you're trying to do is to override theme_facetapi_link_inactive() completely, in which case you don't use a preprocess function, but instead you call the function MYTHEME_theme_function_name() and the theme engine will use that instead of the original function.

So all you need to is change the name of your function like so:

function MYTHEME_facetapi_link_inactive($variables) {
  // Same code as in your example
}


After you clear the caches Drupal will start using that function in place of theme_facetapi_link_inactive() whenever it's called.