  We study the low temperature static and dynamical properties of the classical
bond-disordered antiferromagnetic Heisenberg model on the kagome lattice. This
model has recently been shown to host a new type of spin liquid exhibiting an
exponentially large number of discrete ground states. Surprisingly, despite the
rigidity of the groundstates, we establish the vanishing of the corresponding
spin stiffness. Locally, the low-lying eigenvectors of the Hessian appear to
exhibit a fractal inverse participation ratio. Its spin dynamics resembles that
of Coulomb Heisenberg spin liquids, but exhibits a new low-temperature
dynamically arrested regime, which however gets squeezed out with increasing
system size. We also probe the properties of the energy landscape underpinning
this behaviour, and find energy barriers between distinct ground states
vanishing with system size. In turn the local minima appear highly connected
and the system tends to lose memory of its inital state in an accumulation of
soft directions.
