Regular glass does not have a stressed layer, but tempered glass is made in such a way that its outer surfaces are in compressive stress. Neither regular glass nor tempered glass has an intentionally made “weak” layer.
Perhaps it would help to understand the way both types are made. First, you must remember that glass is very weak in tension, and very strong in compression. When you bend a piece of glass, the surface that is on the inside of the bend is in compression, but the surface on the outside of the bend is stretched and therefore in tension. Cracks start at the outside surface, and once the crack starts, the glass breaks.
Tempered glass (sidelites/side windows on automobiles) is made by taking a very hot, nearly molten sheet of glass and cooling it very rapidly (usually by exposing it to a blast of cold air). This instantly cools and freezes the outer surfaces, while the inner part is still nearly molten. Then, as the glass sheet fully cools, the inner part shrinks, but since the outer surfaces were already cold and hard, the shrinking inner part causes the outer surfaces to be stressed in compression. So once totally cool, the inner part is “normal” glass, but the outer surfaces are highly stressed in compression. When you bend a piece of tempered glass, the outer surface that normally “sees” tension, is already in compression, and so resists the tensile stresses, and therefore resists cracking and breaking.
Normal glass (door walls in your home) is cooled very slowly, and therefore has no stresses. As a result, as soon as it is bent, tensile stresses occur and breakage results.