  The stable fragmentation with index of self-similarity $\alpha \in [-1/2,0)$
is derived by looking at the masses of the subtrees formed by discarding the
parts of a $(1 + \alpha)^{-1}$--stable continuum random tree below height $t$,
for $t \geq 0$. We give a detailed limiting description of the distribution of
such a fragmentation, $(F(t), t \geq 0)$, as it approaches its time of
extinction, $\zeta$. In particular, we show that $t^{1/\alpha}F((\zeta - t)^+)$
converges in distribution as $t \to 0$ to a non-trivial limit. In order to
prove this, we go further and describe the limiting behavior of (a) an
excursion of the stable height process (conditioned to have length 1) as it
approaches its maximum; (b) the collection of open intervals where the
excursion is above a certain level and (c) the ranked sequence of lengths of
these intervals. Our principal tool is excursion theory. We also consider the
last fragment to disappear and show that, with the same time and space
scalings, it has a limiting distribution given in terms of a certain
size-biased version of the law of $\zeta$.
