We report deviations from an ideal behavior of binary chalcogenide glass composition Ge20Te80 with respect to its quenching rate on mass density and thermal parameters, including glass transition temperature. In an ideal glass, the increase in quenching rate will decrease the characteristic relaxation time and correspondingly shift in the glass transition temperature (T-g) to higher temperature and result in lower density. This, however, holds only when the liquid structure remains the same as in equilibrium glass structure independent of their quenching rate. We find Ge20Te80 glass composition with higher quenching rate is found to possess larger density and lower Tg than the lower rate quenched or well annealed glass specimen. In contrast to conventional glass forming liquids, the anomalous behavior of Ge20Te80 glass with respect to quenching rate is closely related to the change in the local atomic structure with thermal history. Additionally, we found that crystal derived from the GemTem glass with different thermal history but with identical annealing conditions leads to different mass density, specific heat capacity, and local atomic structure. Thus, the observed unusual variations in the mass density and various thermal properties of Ge20Te80 glass and crystal are mainly determined by the resulting local atomic structure and concentration of defect states associated with each state.