  We numerically study quantum avalanches in 1D disordered spin systems by
attaching two XXZ spin chains. One chain has low disorder representing a rare
Griffith's region, or thermal inclusion, and the second has larger disorder,
i.e. disorder larger than the observed finite-size crossover. Comparing
dynamics of this system to identical systems with uniformly large disorder, we
find evidence for exponentially slow thermalization (in disorder) within the
MBL regime when the rare region is present. We observe a decay of the spin
imbalance in the bulk of the large disorder region that persists to long times
($\sim10^{4}$) and find a universal behavior of the spectral function.
