I regularly browse the usual auction sites both in Europe and the US (Juliens etc.) for any props that may still be around from the classic series. Unlike many other shows from the same era, it is rare indeed to come across props from the show. Did Lorimar destroy everything? We know Larry procured some items that were sold many years later, but there is very little out there. The last item that I recall was Bobby's bath robe! And it wasn't even the polka dot one to match his shirt. Speaking of props, here's a pic of my office door at home.
Like most movie studios, Lorimar reused most of the props. picture cars and set dressing items in other productions. We have a whole section of cross-references of that kind:
https://www.falconcrest.org/english/master.php?path=show/productionoffice/beyond — although it is written from the perspective of "Falcon Crest", you will find some relations to "Dallas", "Knots Landing" and other shows. Warner Bros., as successor-in-interest to Lorimar, still has many of the props from those shows in their prop department. They are not only available for their own productions, but also on a rental basis to other industry professionals.
Usually, props and sets that were highly specific and easily recognizable did not get reused, but were either changed and redressed (the usual thing for set elements) or destroyed (like the faux stained glass replica of the Falcon Crest Victorian Mansion front doors, stairway window and the other "usual" stained glass window which was constantly moving around in the Mansion wherever they needed it).
Some pieces were given to staff and crew members or the cast, particularly if the requested them. Some cast members had a wardrobe deal in their contracts and were free to keep their clothes from the show (but that was limited to just a few people); most clothes were altered and reused for other purposes, some were sold off.
Of course, some other props were sold over time, either to other studios or in auctions. Since so much time has passed since these shows were filmed, there are not many props left that circulate on the open market.