A unique feature of transition metal dichalcogenides is their single-layer form, which enables folding. Although folding has been found to significantly affect the photoluminescence spectrum and some in-plane properties, only limited insight has been gained on how to modulate those properties. In this report, we examine the structure of folds of a single sheet of MoS₂ and the dependence of the ground-state electronic and phonon transport properties on the wrapping length. As the folded structure is effectively a bilayer that terminates in a loop, the wrapping length modulates the relative size of the bilayer region to the closed loop along the edge. A combination of computational methods, including approaches based on variational mechanics, classical potentials, and density functional theory, are employed. Highly accurate calculations of the reference folded structure are first carried out to show that the folded structure is largely insensitive to the wrapping length. The folded structures are subsequently used to estimate the electronic band gap, which is found to vary significantly as a function of the wrapping length, and converges from below to the limit value corresponding to an infinite bilayer. The gap values range from 0.43 to 1.09 eV, with a crossover to an indirect gap, which suggests that the transitions must be lattice-assisted, similar to the transitions in the bilayer and bulk forms. However, the phonons, while affected by the formation of the folded structure, are insensitive to the wrapping length. In fact, the overall thermal transport behavior along the folding axis is unchanged. The possibility of modulating the gap value while keeping the thermal properties unchanged opens up new exciting avenues for further applications of this emerging material.