Epsilon near near-zero (ENZ) materials have been raising significant interest in various research areas. Rich concepts such as photonic doping an d supercoupling featuring ENZ materials have been reported. ENZ materials have been proven to be instrumental to ach ieve embedded eigenstates, or self self-sustained electromagnetic resonances in open structures with momentum compatible with the radiation conti nuum. However, unavoidable absorption in realistic ENZ materials results in a finite lifetime of these modes, and de cay to radiation. Here, we present a strategy to tackle the losses of ENZ materials in order to produce unbounded high high-Q resonances with the use of PT -symmetry and the concept of suppressed leakage. These results pave the way to efficient light trapping an d sensing applications with realistic ENZ materials.