Esbern is a member of the blades and a former homeless. Cock and Esbern have been fellow homeless for a while.
Esbern enters the story after Cock finds victims of a drive by shooting and loots them. One of the items in the loot was a letter addressed to a Thalmor stripper and mentions Esbern.
Cock goes to meet Esbern, his old homeless friend, in the Riften ratways. At first Esbern does not notice Cock Nibbler. Cock reminds him about the good old days of being homeless with his pal Esbern but after speaking for a while, Cock mentions Dragonborn. This seemed to jog his memory. Esbern and Cock fights Thalmor agents to get out of the ratways and visit Delphine.
Cock introduces Esbern to Delphine but he realizes that they already knew each other somehow. At first Cock thinks that maybe Delphine was homeless once too. However, Cock later realizes that Esbern and Delphine met at a job. In fact, he got a job at the blades protecting the empire. Cock is disappointed that his old friend is no longer a true homeless, a homeless that doesn't accept money..
In search of an elder scroll, Cock Nibbler goes talk to Esbern. Esbern advises you to go to the College of Winterhold. This evokes memory of Cock's days at Homeless U. He and Esbern was on the Homeless U football team but the College of Winterhold beat them because they weren't homeless and had resources.