Semiconductor membranes emerged as a versatile class of nanomaterials to control lattice strain and engineer complex heterostructures enabling a variety of innovative applications. With this perspective, herein this platform is exploited to tune simultaneously the lattice parameter and bandgap energy in group IV GeSn semiconductor alloys. As Sn content is increased to reach a direct bandgap, these semiconductors become metastable and typically compressively strained. It is shown that the relaxation in released membranes extends the absorption wavelength range deeper in the mid-infrared. Fully released Ge 0.83 Sn 0.17 membranes are integrated on silicon and used in the fabrication of broadband photodetectors operating at room temperature with a record wavelength cutoff of 4.6 µm, without compromising the performance at shorter wavelengths down to 2.3 µm. These membrane devices are characterized by two orders of magnitude reduction in dark current as compared to as-grown strained epitaxial layers. A variety of experimental tools and optimized calculations are used to discuss the crystalline quality, composition uniformity, lattice strain, and the electronic band structure of the investigated materials and devices. The ability to engineer all-group IV transferable mid-infrared photodetectors lays the groundwork to implement scalable and flexible sensing and imaging technologies exploiting these integrative, silicon-compatible strained-relaxed GeSn membranes.