In the framework of the SuperEMFL (Super European Magnetic Field Labs) project, we have previously studied numerous possible pre-designs made of an HTS insert with a LTS outsert to achieve a central magnetic induction of 32 T and 40 T. From the most interesting designs, the behavior of the magnet has been studied during the quench of one of the superconducting parts, either LTS or HTS one. This study includes a multi-physics analysis (magnetics, thermics, mechanics) of both parts and has been led with two different codes, each one based on a very different protection principle. We showed that the quench of the LTS outsert, as it is adequately protected, caused a quasi-symmetrical quench of the HTS part, with a limited increase of the temperature. However, the ignition of the quench within the HTS insert leads to an asymmetrical current distribution and to a significant axial force resultant generated on the LTS part. This may necessitate mechanical reinforcement to address the resulting imbalance.