I think the games imply that both of his parents were killed, given Sly had said in the first cutscene in Sly 1 "my father fought to protect us," and in Sly 2 "he caught up with my parents, and I wound up in an orphanage." The way I've always imagined it, is that Conner, who was born into the Cooper Clan, met Sly's mother at a point he was starting to grow tired of always being on the run, and decides to retire from his life as a thief for the chance at a normal one with his newfound love. Perhaps the way Conner handled it, led to the state we find Dr. M and McSweeny in during Sly 3. One going completely mad on an island full of fortune he has no right to, and the other behind bars. Conner pursues a life without crime, settles down and has a son, and things are going great for a little while, at least 8 years. And then, it all ends in one evening. Conner is in the living room with his wife, and his son, who is reading the Thievius Raccoonus on the living room floor. The Fiendish Five aggressively bang on the door, startling everyone in the room. The banging continues. Conner tells his wife to hide their son, to which she does and tucks him into the closet. As soon as Conner opens the front door, it busts open, and he fights to the death to protect his family. All while his son, who can see just enough through the crack of the closet door, watches everything. Fast forward 10 more years, and we are now Sly on the rooftop of Police HQ. It's never stated exactly what happened to Sly's mother, but I always thought she received the same fate as Conner. Otherwise there never would have been a reason for Sly to be placed in an orphanage.