The brick and mortar equivalent of pushing search results to page 2 is to just stop carrying the product—considerably worse than being on page 2.
But no plausible deniability.
Amazon does not purchase most of the inventory listed in its search results.
Retail stores actually buy (almost) everything they sell (albeit at lower "wholesale" prices), and "resell" to end customers. So when a retail store stops carrying a product, they stop buying the product from the supplier, and that is always because the item was not profitable to sell.
(In rare cases, they sell on consignment, but such arrangements would apply to less than .001% of products sold at retail. Selling on consignment has a whole host of separate issues, which is why it is so rare even though it would seem most profitable to retail stores.)
This is true in general, but not absolutely true.
In some cases, manufacturers rent shelf space from stores, then pay the store a commission for each unit sold.
Various power tool manufacturers use this model, the name of which eludes me at this moment. I think Moleskine also does it.
Vendors do not cover shrinkage, except for the rare items sold on consignment. Shrinkage losses are either absorbed by the store or handled by insurance.
But that is the exception that proves the rule, and suppliers go into those situations with the option of simply selling to competing retail stores.