Fixed rigging stays with the anchor. In canyoneering, fixed rigging gets left behind for the next group to use/remove. In caving, you remove the rigging after you've ascended back up that drop.
Fixed rigging should be ERNEST:
Equalized - the load is distributed equally among the anchors
Redundant - a single failure does not result in catastrophe
Non-Extensible - a failure of one anchor does not result in the rappeller falling a short distance and shock loading the remaining anchors
Solid - each component mush be solid enough for the situation