The Cat was a stray cat adopted by Tony Soprano which is brought to Satriale's during the final episode of the show.

The cat looks at Christopher’s picture on the wall in Satriale's Pork Store.
History[]
Tony found the cat at the safe house he was staying at during the war with the Lupertazzi Family; it showed up in a snowstorm and caught a mouse in the basement during its first night. Tony kept the cat and brought it to Satriale's Pork Store, when he and his gang are able to return there after the sit-down. Paulie Gualtieri is shocked to see the cat and wants to get rid of it, and Tony tells him he found it at the safe house and brought it to catch mice and he’s a good cat. The cat stared at Christopher’s picture on the wall, which concerns Paulie- still determined to get rid of the cat. Paulie waves a broom at it before Tony enters, and masks his actions with the broom by pretending to sweep the floor; Walden Belfiore takes the cat with him outside. One day when Paulie is sitting outside Satriale’s, the cat shows up and lies down on the sidewalk. ("Made in America")
Symbolism of the Cat[]
The cat serves as a symbol of foreshadowing. A very important part of the episode ("Made In America") that most people tend to not notice or overlook. When Tony is speaking with Neil Mink over lunch, Neil tells Tony "that someone is giving the grand jury testimony on something". In all likelihood, the individual in question is Carlo Gervasi. As Neil speaks, he repeatedly slaps the back of a Heinz ketchup bottle, mimicking the echoing of gunshots as he glances away effortlessly at Tony's security monitor, observing the Bing girls, unknowingly revealing the fate that lies ahead for Tony and Paulie. Not only does the cat serve as the basis of Tony Soprano’s guilt for killing Christopher Moltisanti, it also serves as a forewarning for the upcoming demise of both Tony and Paulie.
When Paulie confesses to Tony, sitting beside him outside of Satriale's, that he had a paranormal encounter with the Virgin Mary at the Bada Bing after seeing Eddie Lin (Season 6, Episode 9 "The Ride"), Tony disregards him, telling him "Why didn't you say something?". Tony being the sociopathic jerk with a lack of empathy, that he can be at times, proceeds to disregard his experience, telling Paulie, "Fuck the strippers, we could've had a shrine. Sold holy water in gallon jugs. Could've made billions", thus laughing it off. Paulie being upset, tells Tony, "I tell you something deep from my heart, and you laugh it off?". Tony then tells him that he would rather offer a job of running the seemingly cursed Aprile crew to his soon-to-be co-father-in-law Patsy Parisi instead of Paulie for not being able to move on. In turn, Paulie calls Tony a "prick" and says to him, "You always know what to say to me, don't you?". We see a face of fear in Paulie's eyes as he turns away from Tony, only to look back up to him and say, "I live but to serve you, my liege", and then looks down in sadness as he realizes that in the life, the outcome of one's fate will always be determined by actions and the consequences that come with them. When you're in, there's no going back. We see Paulie concerned, shrugging it off and resuming his sun tan regimen, while the cat, appears out of nowhere. And lays right next to Paulie. The implication that, as with "The Godfather" the color orange represents death.
In several episodes of The Sopranos, Tony has stated that there are only two ways out for a high-profile mob boss: dead or in jail. He says it in season 2, episode 6, "The Happy Wanderer". By the end of the series, Johnny Sack dies of lung cancer in jail, leaving another warning of what lies ahead for Tony and Paulie for their misdeeds in the life. The cat is laying next to Paulie, implies that that's how his body will be left to lay on the ground, in a pile of blood and riddled with bullets. And Tony is up next. In a way, it's possible that the spirit of Christopher has harbored the vessel of the cat, already aware of the eventual outcome of their fates, which could be interpreted as revenge from the great beyond, as he was holding a bitter grudge against them even in death for how they mistreated him in life. The cat from a spiritual viewpoint, represents power and murder.
In the beginning of The Godfather, Vito Corleone is playing with a cat while speaking to undertaker Amerigo Bonasera, who asks him to put a hit on the men who assaulted his daughter, on the same day of Don Vito's daughter's wedding. Cats also symbolize predatory nature, as they always come by surprise, much like many of Tony's own hits.
Behind the Scenes[]
The cat is played by 3 different cats who’s names were Timmy, Tommy, and Terry who were well trained by Debbie Pearl for paws for effects.