  Lattice defects such as stacking faults may obscure electronic topological
features of real materials. In fact, defects are a source of disorder that can
enhance the density of states and conductivity of the bulk of the system and
they break crystal symmetries that can protect the topological states. On the
other hand, in recent years it has been shown that lattice defects can act as a
source of nontrivial topology. Motivated by recent experiments on
three-dimensional (3D) topological systems such as Bi$_2$TeI and
Bi$_{14}$Rh$_3$I$_9$, we examine the effect of stacking faults on the
electronic properties of weak topological insulators (WTIs). Working with a
simple model consisting of a 3D WTI formed by weakly-coupled two-dimensional
(2D) topological layers separated by trivial spacers, we find that 2D stacking
faults can carry their own, topologically nontrivial gapless states. Depending
on the WTI properties, as well as the way in which the stacking fault is
realized, the latter can form a topologically protected 2D semimetal, but also
a 2D topological insulator which is embedded in the higher-dimensional WTI
bulk. This suggests the possibility of using stacking faults in real materials
as a source of topologically nontrivial, symmetry-protected conducting states.
