The sampling of the wave function within a suitable ensemble is an important tool in the statistical analysis of a molecule interacting with its environment. The uniform statistical distribution of quantum pure states in an active space is often the privileged choice. However, such a distribution with constant average populations of eigenstates is not preserved upon the interaction between quantum systems. This appears as a severe methodological shortcoming, as long as a quantum system can be always considered as the result of interactions among previously isolated subsystems. In the present work we formulate an alternative statistical ensemble of pure states that is robust with respect to interaction, and it is thus preserved when subsystems are merged. It is derived from the condition of invariance of the average populations upon interaction between quantum systems in the same thermal state. These average populations allow a simple identification of the thermodynamic properties of the system. We find that such a statistical distribution is robust with respect to interaction of systems at different temperatures reproducing the thermalization of macroscopic bodies, and for this reason we identify it as the Thermalization Resilient Ensemble.