A solution is developed to overcome the low-frequency breakdown of a full-wave finite-element-based analysis of general lossy problems, where the dielectric and conductor loss can co-exist and both are inhomogeneously distributed. This solution is rigorous from high frequencies all the way down to zero frequency. It explicitly reveals the frequency dependence of the field solution in general lossy settings, based on which a fast solution is also developed for solving the low-frequency breakdown. Numerical experiments have validated the proposed method.