Show facet filter even if there is no result Is there a way to show the facet filter, even if the Search API module returns no result?
Not really, the facets (both search api and solr) are made up from the results of the search, therefore if there are no results then it doesn't know what to populate the facets with.

Depending on your expected output you may be best creating a custom/views block to display some relevant content then re-write the urls to conform with the search query, acting like a search facet.