The popover and dialog displayed by FacetFilter contain an sap.m.SearchField control. This enables the user to search for specific items in the list.
FacetFilterList internally handles the search and liveChange events by filtering the underlying data model: The search only works when the FacetFilterList items aggregation is bound to a model.
If you enable the liveSearch property of the FacetFilter control, keep the performance in mind as this will result in a backend request for each search character typed by the user.