There’s a well-established agreement between brands and influencers: We send free products, you post about them on Instagram. Often it’s a happy arrangement; influencer feeds fill with promotional material, followers click and merchandise sells. But sometimes the posts never appear.

When this happens, the brand’s representatives may assume the “entitled” influencer has either kept the product or tossed it disapprovingly without so much as a “thank you.” But now another possibility has emerged: The brand might have been defrauded by an impostor.

Scammers, using throwaway email accounts and fake websites, are pretending to be influencers (or their assistants), requesting free products in exchange for prominent billing on a highly trafficked Instagram feed. Some companies, unaware that the contact is a fraud, will send up to thousands of dollars worth of merchandise to a specified address. The deception comes at a cost to both the brand and the influencer.

Jeanne Grey, who posts about fashion and beauty as @TheGreyLayers, experienced this niche form of identity theft earlier this summer. “It has been made aware to my team and I that there is someone who is using my likeness and identity to reach out to brands,” she wrote to her more than 461,000 followers via Instagram Stories in July. “I have received multiple emails from brands that I’m friends with and new brands of this, most of which have fallen for it and sent out products for free.” (Ms. Grey declined, through her lawyer, to speak to The New York Times.)