I attacked and conquered the only planet of a minor race which had two mining starbases (i.e., bases held two interstellar resource points). After the race was destroyed, its bases disappeared...but so, in some ways, did the resources it was using. They still appear on the map--but a mouseover on the icon shows no popup with info/description, and a constructor ship can't mine the sector. Construction is limited to the same 3 options you have in any other sector (military, economic, influence).

If the resources are truly gone, they shouldn't show up as icons on the map. If they are not gone, they should be exploitable again.