There is "commercial crime insurance" (separate from general business insurance) but I can't imagine an underwriter staying in the San Francisco market. And a large retailer like CVS, Walgreens, or Target would almost certainly be self-insured.

Are you using “self-insured” as a euphemism for “just eats the losses”? Because it’s not really insurance if there’s no risk pooling, and a large retailer is a single entity—who are they pooling risk from? Individual stores? That would make sense only if they are franchises.

That’s basically what self-insured is. Large employers offer health insurance but they aren’t pooling risk with other companies, they just pay all expenses.

Insurance is meant to protect against catastrophic loss. If a loss isn’t catastrophic, it’s often cheaper to just pay for the loss yourself.

It is a well-defined term: https://www.investopedia.com/terms/s/self-insure.asp

They may not be pooling risk, but they may be hiring actuaries to look at their past losses compared to similar businesses, and setting aside a reserve to cover expected future risk.

I’m sure that’s exactly what they do, but that’s not insurance—just prudent risk management.

"Does insurance pay out for shoplifting?" <- Yes and no. If you file a claim to the insurance company they will probably pay out. But they are trying to turn a profit too - if you are filing too many claims in a specific area they will just drop you.

Insurance pays out for theft even without a police report as long as it is a specific event (very common e.g. for shipping, where sometimes it isn’t even known in which country the theft happened). I have never heard of a policy covering “shrinkage”.