There are 2 templates being used for result, one for simple search ( using top search field ) and other is for advance search field :
For Top search field result :
module_catalog-search/view/frontend/templates/result.phtml
For Advance Search result :
module_catalog-search/view/frontend/templates/advanced/result.phtml
And both search fields search data / record within product catalog, override the template(s), and add your condition in that template to show whatever data you want to show if there is no record is returned.
