They exist. I knew a fantastic agent (now retired, sadly), with a highly unusual business model. His clients would find a house on their own, via Zillow or whatever. Then they would negotiate a fee structure with the agent. The agent would help them inspect the house, help them negotiate effectively, and did not push for a purchase or a high price at all. If the deal closed, he would take his fee and write the client a check for any commissions from the seller in excess of the fee.

(But he would also offer to try to convince the seller to modify the terms to sell at the same effective received price but without paying a commission and the collect the commission from the buyer. This would usually be favorable from a tax perspective, as including the buyer’s agent fees in the “price” increases the transfer taxes.)

> I've never seen or heard of a real estate agent negotiating to transact a property below its previous sale price

You've never heard of a short sale in which there was an agent involved? (Technically, a short sale is one below the outstanding mortgage, irrespective of the previous sale price, but usually the former will be less than the latter, so...)