Extremely exotic dense matter states can be produced in the interaction of a relativistic femtosecond optical laser with a solid density matter. Here we theoretically investigate triple-core-hole (TCH) states produced by an intense polychromatic x-ray field formed by hot electrons in the interaction of a relativistic femtosecond optical laser with a thin silver foil. X-ray emission spectra of solid-density silver plasmas show unambiguously the production of TCH states at an electron temperature of a few hundreds of eV and radiative temperature of 1-3 keV of the polychromatic x-ray field. Practical calculations show that the emissivity originating from the TCH states exceeds that from the single- and double-core-hole states in Ne-like Ag at electron temperature of ~500 eV and radiative temperature of ~1500 eV. For the neighbouring ionization stages of Ag and Ag , TCH emissivity is roughly equivalent or comparable to that from the single- and double-core-hole states. Present work deepens our insight into investigation of the properties of extremely exotic states, which is important in high energy density physics, astrophysics and laser physics.