  In this paper we work out collapsing conditions for a spherical star in the
weak field limit of the $R+\mu^4/R$ gravity and discuss the importance of the
parameter $\mu$ to generate different criteria in the theory. Such criteria are
proved to be resulting in a variety of different fates for the evolution of the
outer shells of stars. Furthermore, we investigate the special case of
violating the first junction condition and point out corresponding
contradictions to the normal cases. These results show that the consistency of
the $R+\mu^4/R$ theory of gravity with the common astrophysical predictions
relies highly on the adoption of the parameter $\mu$ and satisfaction/violation
of the first junction condition. For those anomalous results, further
observational attempts are mandatory.
