In cases like Horizons the building might remain untouched for a long time. The inner workings like lighting, fixtures, even ride cars and tracks might be reworked and introduced into other attractions. Sometimes the buildings are left alone and simply retrofited into something else, sometimes the buildings are demolished to make way for a new ride.
In either case most things that are unusable for other attrations are scraped, sold or put in storage. Occasionally figures, ride cars or artistic things from old rides make it into private collections or end up on display on or off stage. I think that the actual Horizons sign is still around in an office somewhere and I have seen ride cars on eBay for sale.
