The risk that the business depends too heavily on one person — usually the owner, sometimes a key employee — to keep functioning.
Key-person risk is the dependence of a business on a single individual whose departure would materially harm the company. The most common version is owner dependency, but it also shows up with key employees: the salesperson who owns 60% of customer relationships, the production lead who's the only person who knows how the equipment runs, the technician whose certification the business operates under. Buyers identify key-person risk early because it directly threatens the predictability of post-close earnings. The risk gets priced into the offer, structured into the deal terms, or in extreme cases, becomes the reason the buyer walks away.
Key-person risk shows up in the multiple, the deal structure, the transition requirements, or all three.
Buyers know what every key person walking out the door costs — and they price the deal assuming at least some of them will.