The Suzuki reaction is a coupling reaction between an aryl halide and an aryl boronic acid catalyzed by palladium metal. The first step in this reaction is insertion of palladium(0) into the aryl halide bond forming an oxidized ArPd(II)X intermediate and in the final step Pd(0) reforms from a diaryl palladium species.
This sequence implies that in a suitable heterogeneous system palladium first dissolves and then redeposits. This is where the details get sketchy.
Researchers from Queen's University in Canada have now been able to observe the palladium cycle by heating a tiny section of palladium foil in presence of both reactants and examining the metal surface by scanning electron microscopy (DOI) . They found that palladium disappears at the center of the hot zone and re-deposits in the cooler sections. The aryl halide alone also does the trick emphasizing the similarities with dissolving magnesium metal when forming a Grignard reagent.
In this type of reaction the catalyst is separated from the reaction product by filtration and a better understanding of metal redeposition will certainly help cleaning it up.