It is well-known that a single cluster like Ar-7 undergoes "melting" from solidlike to liquidlike states as the energy is increased, the transition of which is not as sudden as the ordinary phase transition though and has a somewhat broad energy range in which solid and liquid coexist. We study a very anomalous dynamics of the coexistence region in the structural isomerization. It is explicitly shown that the time-series of the structural changes both in the purely solidlike and liquidlike phases are stationary, while the coexistence region is found to generate a strongly nonstationary dynamics. The calculated distribution of the residing times for the cluster to stay in one of the possible structures exhibits a nonexponential form having a large hole around the zero lifetime in the coexistence region. Motivated by these strange behaviors, we have calculated the phase-space volumes that are assigned to the individual potential basins, and verified directly that while the pure liquid region is of ergodic nature, the dynamics in the coexistence region is indeed strongly nonergodic. The steep rises of the Lindemann index and the maximum Liapunov exponent in the coexistence region, which were reported before by other authors, are found to be ascribed to the statistical nature rather than the dynamical properties as opposed to the picture suggested by the physical;meaning of the indices. It also turns out that the energy range for the coexistence region should be taken wider than considered before and thus extends beyond the "melting point" that is defined usually on the basis of the Lindemann index. Therefore it is appropriate to divide the coexistence region into two subphases. A "temperature" in a microcanonical ensemble is defined so as to characterize the distribution of phase-space volume on a given energy plane. Based on this distribution, we describe a statistical reason why the onset energy of the melting is much higher than those of the transition states.