Scrump is Lilo's homemade doll. Lilo made Scrump herself and often has to give her "surgery" after she gets torn. She made her first appearance in Lilo & Stitch and was also seen throughout the franchise. In the Stitch! anime, it is shown that Lilo's daughter Ani inherited the doll.
Scrump, alongside Stitch and Angel, appears in the UniBEARsity story OhanaBEARsity. After seeing Stitch reading the UniBEARsity storybook, she and Angel began making their own teddy bears based on their likeness. Scrump's teddy bear, named Pie, is based on her likeness.
After Lilo picks Scrump up from the ground in the first film, Scrump can be seen smiling behind her back as Lilo walks down the hill.
Despite being an inanimate object, Scrump is treated as a living thing by Lilo (and actually was living when Phantasmo possessed the doll), who refers to the doll as a female. It could be that Scrump is Lilo's "security blanket".
Various merchandise and promotional imagery show Scrump being with Stitch and without Lilo, even though he actually interacted with the doll very few times in the Lilo & Stitch canon.