So, there is this Toy Story theory going around that Jessie's former owner, Emily, and Andy's mom are the same person. The reason being because Emily had a cowboy hat that Andy was seen wearing in the film. They even went as far as to show the hat without the white band around it, illustrating that it's old, therefore losing some of its parts through the ages.
For a refresher (assuming you've all seen the Toy Story films), Emily is seen in this sad-as-[tornado fang] scene.
Toy Story 2 "When She Loved Me" Sarah McLachlan 1999
If I recall, Andy only wore the hat in the first film, while Jessie and Emily were introduced in the second.
Funny how this eluded so many people, me included. Huge props to Pixar for making the viewers look for the hints, without outright telling you that they're the same person and the hat was passed down to her son.