Fylde Guitars has produced guitars without truss rods. Specifically, they designed a neck concept with no truss rod or metal components, relying instead on carbon fiber reinforcement. This design was explored in a guitar where, apart from the tuners and strap pins, no metal was present in the neck.
Here's a more detailed explanation:

    Fylde's Truss Rod Experiment:
    Fylde Guitars, known for its innovative approaches to guitar building, has experimented with necks that don't incorporate truss rods.

Carbon Fiber Reinforcement:
In these guitars, the neck's stability and resistance to bending are achieved through the use of carbon fiber reinforcement.
Minimal Metal Components:
The concept extends to minimizing metal in the neck, with only tuners and strap pins being the exceptions.
"Honest" Design:
Fylde founder, Roger Bucknall, has expressed a preference for this truss-rod-less design, finding it "honest" and simple, and highlighting its effectiveness, according to a Fylde Guitars news article.