Yes a properly designed and built trailer will carry a car safely without you being even aware it is behind you (but luckily you have big West Coast mirrors on your one ton tow truck to monitor your load). Notice how I worked in combined gross vehicle weight?
Your tow vehicle has to be rated for the load you want to carry. A one ton truck has a combined GVW of 10,000 pounds with a 5,600 pounds of that in the truck, and figuring 1,300 to 1,600 pounds of the GVW in the empty trailer weight that only leaves about 3,000 pounds for a vehicle if you are depending upon the tow truck to provide all of the braking. With functioning trailer brakes (electric or self contained hydraulic) you can double that tare weight.
Talking about design: trailer wheels and tires often limit your GVW as a tandem (dual) axle wheel and tire can only hold 6,400 pounds of weight (3,200 pounds per axle) maximum at 45 mph. They are speed limited (six to ten ply side walls that overheat if run faster at full weight). To get a trailer that can carry a car or light truck you need a three axle trailer which will track straighter, but scrub at slow speed while making tight turns.
Of course if you are towing with a another car you are unsafe at any speed.
Funniest thing I ever saw was a little TOYota truck trying to tow a 24 foot power boat on a triple axle trailer with the boat sitting on top of the compact truck (rated at 2,200 pound payload). His 84 horsepower motor could pull it, but the truck lacked enough mass to control the weight of the combined GVW. The boat and trailer just pushed him off the road and into a ditch when he tried to make a sharp left hand turn.