We study the emergence of a fragmented state in a strongly interacting Fermi gas subject to a tunable disorder. We investigate its properties using a combination of high-resolution in situ imaging and conductance measurements. The fragmented state exhibits saturated density modulations, a strongly reduced density percolation threshold, lower than the average density, and a resistance equal to that of a noninteracting Fermi gas in the same potential landscape. The transport measurements further indicate that this state is connected to the superfluid state as disorder is reduced. We propose that the fragmented state consists of unpercolated islands of bound pairs, whose binding energy is enhanced by the disorder.