The self-replicating machine has high utility by virtue of its universal construction properties and its productive capacity for exponential growth. Their capacity is unrivalled. They can be deployed to the Moon to industrialize it using local in-situ resources in the short term to open up the solar system and thence deployed on interstellar spacecraft to explore the entire Galaxy by exploiting in-situ stellar system resources. Nevertheless, there are significant concerns regarding the inherent safety of self-replicating machines. We consider the general problem of runaway population growth in physical self-replicating machines to prevent the grey goo problem, the number of offspring spawned by self-replicating machines may be controlled at a genetic level. We adopt a biologically-inspired approach based on telomeres, DNA endcaps that are progressively shortened during cellular replication. This acts as a counter that imposes a limit to the number of replication cycles (Hayflick limit). By examining the biological process in detail, we can obtain some insights in implementing similar mechanisms in self-replicating machines. In particular, we find that counting mechanisms are vulnerable to cancerous runaway.