Do solid insoluble ions react with soluble ions in aqueous solution?
What you seem to be asking about is a two phase system, a solid phase in equilibrium with ions in solution. For such a system there are two reactions occurring at the same rate. Thus some of the solid is constantly dissolving and some of the ions from solution depositing at the same rate.
There is a named process, Oswald ripening, that describes the interaction in such a solution. The overall effect is that smaller particles are more likely to dissolve so the particle size tends to grow as the process continues since larger particles have a smaller surface area to volume ratio.