  Introduced by Emek and Wattenhofer (PODC 2013), the \emph{stone age (SA)}
model provides an abstraction for network algorithms distributed over
randomized finite state machines. This model, designed to resemble the dynamics
of biological processes in cellular networks, assumes a weak communication
scheme that is built upon the nodes ability to sense their vicinity in an
asynchronous manner. Recent works demonstrate that the weak computation and
communication capabilities of the SA model suffice for efficient solutions to
some core tasks in distributed computing, but they do so under the (somewhat
less realistic) assumption of fault free computations. In this paper, we
initiate the study of \emph{self-stabilizing} SA algorithms that are guaranteed
to recover from any combination of transient faults. Specifically, we develop
efficient self-stabilizing SA algorithms for the \emph{leader election} and
\emph{maximal independent set} tasks in bounded diameter graphs subject to an
asynchronous scheduler. These algorithms rely on a novel efficient
self-stabilizing \emph{asynchronous unison (AU)} algorithm, "thin" in terms of
its state space: the number of states used by the AU algorithm is linear in the
graph's diameter bound, irrespective of the number of nodes.
