  The finiteness property is an important arithmetical property of
beta-expansions. We exhibit classes of Pisot numbers $\beta$ having the
negative finiteness property, that is the set of finite $(-\beta)$-expansions
is equal to $\mathbb{Z}[\beta^{-1}]$. For a class of numbers including the
Tribonacci number, we compute the maximal length of the fractional parts
arising in the addition and subtraction of $(-\beta)$-integers. We also give
conditions excluding the negative finiteness property.
