  We give the Buchdahl stability bound in Eddington-inspired Born-Infeld (EiBI)
gravity. We show that this bound depends on an energy condition controlled by
the model parameter $\kappa$. From this bound, we can constrain $\kappa\lesssim
10^{8}\text{m}^2$ if a neutron star with a mass around $3M_{\odot}$ is observed
in the future. In addition, to avoid the potential pathologies in EiBI, a
\emph{Hagedorn-like} equation of state associated with $\kappa$ at the center
of a compact star is inevitable, which is similar to the Hagedorn temperature
in string theory.
