  We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin
liquid phase, in which quenched disorder leads to random-singlet phenomenology.
More precisely, we argue that a strong-disorder fixed point controls the low
temperature susceptibility $\chi(T)$ of an exactly solvable $S=1/2$ model on
the decorated honeycomb lattice with quenched bond disorder and/or vacancies,
leading to $\chi(T) = {\mathcal C}/T+ {\mathcal D} T^{\alpha(T) - 1}$ where
$\alpha(T) \rightarrow 0$ as $T \rightarrow 0$. The first term is a Curie tail
that represents the emergent response of vacancy-induced spin textures spread
over many unit cells: it is an intrinsic feature of the site-diluted system,
rather than an extraneous effect arising from isolated free spins. The second
term, common to both vacancy and bond disorder (with different $\alpha(T)$ in
the two cases) is the response of a random singlet phase, familiar from random
antiferromagnetic spin chains and the analogous regime in phosphorus-doped
silicon (Si:P).
