We show that standard matter effects in the outer layers of core-collapse supernovae significantly constrain the flavor composition of the neutrino flux, even with the enormous uncertainties originating from self-induced flavor conversions in the supernova core. Under certain conditions, the neutrino flux resulting from self-induced conversions can be represented as a combination of flavor eigenstates in an arbitrary flavor ratio configuration. In this scenario, we find that, for the normal mass ordering, the fraction of neutrinos with electron flavor reaching the Earth, denoted as , is constrained to be less than for all energies throughout the emission phase, whereas, for inverted mass ordering, we anticipate neutrinos arriving in near flavor equipartition (). In case adiabaticity is violated in the region of standard matter effects, the result is flavor equipartition for both mass orderings. Subsequently, we elaborate on the impact of wave-packet decoherence during self-induced conversions and explore alternative scenarios that could affect the aforementioned results.