Not having brake fluid in your car won't destroy the brakes, but whatever you hit when the brakes don't work just might. :)
The brakes in basically every passenger car since the 50's are hydraulically operated. That means when you press the brake pedal you are pressurizing some fluid lines. Those lines run out to the wheels where the added pressure forces the pads against the rotors or drums.
If that fluid is low or missing you will end up with nothing but air in those lines. Air is very compressible, which means when you squeeze it it's volume decreases. The brake fluid in your car is for all intents and purposes incompressible. That means when your foot on the brake pedal operates the master cylinder which squeezes the fluid into the lines that force is transmitted almost completely to operating the brakes. When there is air in the line all you do is move the air around a little and you apply very little force into operating the brakes. When you have only a little air in the lines the pedal just feels "spongy" because you compress the bubbles down to nothing and then you are closing the brakes. When there is a lot of air, or no fluid at all, you just don't operate the brakes at all, and you have a very bad day..
The good news is that topping off the fluid with the right type (DOT-3, DOT-4, and a collection of others are used depending on what car you own) and then bleeding the brakes will bring them right back again. That assumes that when they were dry you didn't end up with any kind of debris in the lines. With no brakes you likely didn't drive it much though.. lol Bleeding the brakes just means opening those hydraulic lines at one wheel at a time and pumping the brakes. That forces the fluid and air through the line and out the tube that's open. Eventually you end up with nothing but fluid and can close that line off and do the same for the others. There's a bit more to it, but that's the simplified version.
Bottom line, unlike your engine where the fluid is a lubricant, in your brakes the fluid is a hydraulic fluid. So it's not a catastrophic destruction when it's low, just needs to be properly maintained and you're back on the road.
Hope that helps!