According to Trex manual on how to properly install Trex composite boards, you should never install Trex on top of existing deck flooring. That being said, existing deck framing and joists are perfectly usable to resurface with Trex decking - as long as the framework is stable and in a suitable condition. The anatomy of a deck consists of the footings, posts, beams, and joists. All of these components are equally important pieces to the structure and determine the life expectancy of that deck.
Trex composite decking is expected to last a home's lifetime. It only makes sense that the framework holding up that decking lasts just as long. When a deck is being resurfaced, it’s undergoing partial demolition, and partial replacement. The floorboards, railings, stair surfaces, and fascia are all torn off and disposed of. Following the demo, your deck builder should perform a thorough check of the integrity of each piece of the deck’s frame. It’s common that when a deck’s surface is due for a replacement, the structure it’s fastened to is also showing some wear and tear. Commonly, 10% of existing joists are in need of replacement. A handful of perimeter boards may need replacement as well, so the new fascia and deck flooring can be installed properly.
What matters most is that the integrity of the frame is just as strong as the new Trex composite decking that is laid on top of it.