What is the no overload region of a quantizer?
It is stated in chapter 5 (Scalar Quantization I: Structure and Performance) of the book "Vector Quantization and Signal Compression" by Gersho-Gray that


  Associated with every $N$ point quantizer is a partition of the real line
  $\mathcal R$ into $N$ cells or atoms $R_i$, for $i = 1,2,\cdots, N$. The $i$th cell is given by $\mathcal R_i=\{x \in \mathcal R: Q(x) = y_i\} \equiv Q^{-1}(y_i)$, the inverse image of $y_i$ under $Q$. It follows from this definition that $\bigcup_i \mathcal R_i = \mathcal R$ and $R_i\bigcap R_j = \emptyset$ for $i \neq j$. A cell that is unbounded is called an overload cell. Each bounded cell is called a granular cell. Together all of the overload (granular) cells are called the overload region (granular region).


So in other words, the union of bounded regions (i.e. granular region) where saturation does not occur is referred to as the "no overload" region and is identified in the following picture