What can a seller actually do if a buyer breaches the exclusivity clause?

This depends on how the exclusivity clause was actually drafted, since most exclusivity provisions restrict the seller from shopping the business rather than placing a matching obligation on the buyer. If your specific LOI does impose a reciprocal or parallel restriction on the buyer — for example, an obligation not to use shared information to pursue a competing acquisition, or a non-solicitation commitment covering your employees or customers during the period — a buyer breaching that specific promise is what you'd actually be pursuing, not a breach of "exclusivity" in the sense most people mean it.

Where a genuine buyer-side breach exists, the seller's practical remedy is generally a claim for damages caused by that specific breach, though quantifying loss can be difficult, since the underlying deal was never guaranteed to close anyway even without the breach. Some LOIs address this directly with a specified remedy, such as cost reimbursement, for exactly this kind of situation, which is far more useful than relying on general contract principles after the fact.

Before assuming what recourse you have, check precisely what obligations your LOI actually placed on the buyer, and have a Treadstone business lawyer assess whether what happened breaches something specific and enforceable.