  We revise the expansion history of the scalar field theories known as Kinetic
Gravity Braiding. These theories are well-known for the possibility of driving
the expansion of the cosmos towards a future self-tuning de Sitter state when
the corresponding Lagrangian is invariant under constant shifts in the scalar
field. Nevertheless, this is not the only possible future fate of these
shift-symmetric models. Using a dynamical system formulation we show that
future cosmological singularities can also appear in this framework. Moreover,
we present explicit examples where the future attractor in the configuration
space of the theory corresponds to a big rip singularity.
