The abyss is the name given to the empty area underneath the terrain in Driv3r. If you accidentally enter the abyss, you will fall for a few seconds and land on a flat surface, before promptly dying from the fall damage. This glitch is similar to the Blue Hell glitch in Grand Theft Auto games.
If the player has the invincibility cheat enabled, he will be able to fall through the abyss and land on the solid surface at the bottom without dying, but then he will be unable to "escape" the abyss, unless he restarts the game.
The player is not supposed to access the abyss, but there are terrain glitches in the gameworld which the player can accidentally fall into. The Police Station in Miami has several unsolid sections of terrain around it as well as inside of it, which the player can fall through. The Armory and Nice's Airport have abysses which you can fall into. The one at Nice's Airport is the one in the grass. You could be driving on the grass and you fall in a hole as if you were sucked in quicksand.You'll land on an invisible plane below the actual ground. Don't drive your car on the black walls; it'll explode and kill you. Abysses are found in many different places so watch where you're walking.