To find the integer that makes the addition sentence true, we can set up the equation based on the given statement:
\[ -16 + x = -32 \]
To solve for \( x \), we can add 16 to both sides of the equation:
\[ x = -32 + 16 \]
Calculating the right side gives:
\[ x = -16 \]
So, the integer that makes the addition sentence true is:
\[ \boxed{-16} \]