The structure of clusters of two-dimensional particles interacting with a hard-core square-well pair potential is analyzed in order to demonstrate how thermodynamic stability ceases to exist when the system approaches the Baxter’s sticky limit, It is shown that the dependence of the sizes and the radii of gyration of the clusters of two-dimensional sticky disks behave qualitatively differently when the number of particles in tile cluster exceeds 6, Cluster sizes with n < 7 exhibit smooth transition when the Baxter limit is approached while clusters with seven more disks experience an anomalous transition towards a state of maximal connectedness. The configuration integrals that are needed to describe clusters of seven particles are then used to demonstrate the way in which their contribution to the virial expansion of the equation of state causes it to become pathological. From the results, it is concluded that the system will show the anomalous thermodynamic behavior associated with the approach to instability only for well widths of the order of 10(-4) of the hard core diameter or less, The status of using approximate adhesive-particle results as approximate square-well-particle results is then summarized, It is pointed out that there is a fundamental defect in all currently available methods of approximating square-well liquid-gas phase separation using adhesive-sphere results.