Supported catalysts are important tools for developing green-economy-based processes. Palladium nanoparticles (NPs) that are immobilized on two fibers developed as metal scavengers (i.e., Smopex®-234 and Smopex®-111, 1% w/w) have been prepared and tested in copper-free cyclocarbonylative Sonogashira reactions. Their catalytic activity has been compared with that of a homogeneous catalyst (i.e., PdCl2(PPh3)2). Pd/Smopex®-234 showed high activity and selectivity in the synthesis of functionalized heterocycles, such as phthalans and isochromans, even when working with a very low amount of palladium (0.2–0.5 mol%). The extension of Pd/Smopex®-234 promoted cyclocarbonylative reactions to propargyl and homopropargyl amides afforded the corresponding isoindoline and dihydrobenzazepine derivatives. A preliminary test on Pd NPs leaching into the solution (1.7 × 10−3 mg) seems to indicate that, at the end of the reaction, almost all of the active metal is present on the fiber surface.