Prerift salt layers associated with extensional detachment faults exhuming mantle and deeper crustal rocks at the sea floor are observed in the Parentis and Arzacq-Mauleon basins located at the eastern termination of the Bay of Biscay. How detachment faults interact with salt in hyperextended rift systems is yet little understood. Based on field observations and drill-hole and seismic data, we propose a new model to explain the interaction between salt tectonics and extensional detachment systems. We demonstrate that the presence of a thick prerift salt layer in an area undergoing extreme crustal thinning can control the geometry and evolution of rift systems and obscure the rift-related structures in the underlying basement. During an initial stage of rifting, prerift salt layers act as a decoupling horizon between sub- and suprasalt units and hinder crustal detachment faults to cut through the salt layers and form breakaways at the sea floor. As a consequence, they sole out along the ductile salt layer and no subsalt material can be exhumed to the sea floor. Thus, sub- and suprasalt layers deform by different deformation modes, which makes that detachment fault difficult to identify on seismic images. In a later stage, when salt has migrated and thinned out, sub- and suprasalt layers can locally couple and detachment faults can be exposed at the surface, resulting in windows of exhumed basement surrounded by extensional allochthons formed by suprasalt sedimentary units.