The bonding between sodium and chloride ions comes from their strong attraction. It is not a covalent bond and so doesn’t pair up specific atoms except to make sure the charges balance. It’s going to attract any two sodium ions equally as long as they’re both the same distance away.
If you introduced a solution of potassium iodide at the surface, the potassium ions would fill the same purpose as the sodium ions and so easily swap place. No bonds are breaking – the iodide ions are present in the outside solution to serve the same purpose as the chloride ions in the solid.
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