Drupal 7 Faceted Search: Always show Facets
Under admin/config/search/search_api click “edit” on your search index and select “Facets”. Then for all facets that need the described behavior for their items, follow these steps:


Click “configure display”.
In the “Global settings” section, change the “Minimum facet count” to 0 (zero). Arguably this input field should rather be called “Minimum facet item count” …
“Save configuration”.


Now all non-matching facet items should remain in your facet list (with a zero count). As you have already mentioned, clicking such a facet item will return no search results anymore.