The synthesis of silver nanowires in solution phase is of great interest because of their applicability for fabrication of plasmonic devices. Silver nanowires with diameters of 6.5 nm and length exceeding microns are synthesized in aqueous solution by reduction of silver ions within the nanotubular J-aggregates of an amphiphilic cyanine dye. The time scale of the growth of the nanowires is of the order of hours and days which provides the unique possibility to investigate the nucleation, growth, and dissolution of the nanowires by direct imaging using transmission electron microscopy. It is found that the initial nucleation and formation of seeds of silver nanostructures occurs randomly at the outer surface of the aggregates or within the hollow tube. The growth of the seeds within the inner void of the tubular structures to nanowires indicates transport of silver atoms, ions, or clusters through the bilayer wall of the molecular aggregates. This permeability of the aggregates for silver can be utilized to dissolve the preformed silver wires by oxidative etching using Cl- ions from dissolved NaCl. Although the nanosystem presented here is a conceptual rather simple organic-inorganic hybrid, it exhibits growth and dissolution phenomena not expected for a macroscopic system. These mechanisms are of general importance for both, the growth and the usage of such metal nanowires, e.g. for plasmonic applications.