The advantage of mapping modified gravity theories with standard matter into general relativity (GR) with modified matter is that we can quickly implement the well-established analytical and numerical methods developed within GR to study modified gravity theories and compare the modified gravity theories with current observational data. In this paper, we explicitly show that overturning/cracking instability may occur in an isotropic Eddington-inspired Born-Infeld (EiBI) stellar structure. Analyses are done by reducing the Tolman-Oppenheimer-Volkoff-like equations of EiBI into the ones of GR with an additional anisotropiclike nonlinear term. We obtain the term by expanding the stellar structure equations with respect to γκϵ and γκP and by using numerical calculations. We find that, for a specific value of κ, the overturning/cracking may occur. In the nonrelativistic regime, cracking tends to occur when κ>0. In the relativistic regime, for neutron stars (NS) with equation of state (EOS) based on a relativistic mean field model (RMF), the overturning occurs at κ0, and the overturning point is located near the core of the star. We also show that the stellar structure equations within EiBI theory with isotropic matter can be recast into GR defined in a physical metric g with a modified (apparent) anisotropic matter. In this representation, the signature of a potentially overturning instability within the apparent anisotropic structure is present and related to the asymptotic behavior of the apparent speed of sound near the center of the star and an imaginary value of the apparent tangential speed of sound near the edge of the star.