Most DC who steal are missing out on something somewhere.
I agree with this - in spades! This is either a very troubled or a very entitled child.
But either way I would not have her back in the house (something similar happened to my DD - not a friend, but the sister of a friend - my DD was totally heartbroken. Not by the loss itself - the monetary value was negligible (about £3.00 - easily replaced*), but by the fact that someone she knew, who she had played with and considered to be a friend, had done this.
I mentioned it to her mother (In a "I wonder if DD has left XXX at your house? She's come back today and didn't have it with her? Would you mind keeping your eyes open in case it's under a bed/settee/in a cupboard etc " A day later she said I couldn't find XXX, but I know MyDD didn't take it (I hadn't suggested that she had, though that was what I believed) because when she takes stuff she admits it".)
Some years later I discovered that my DD wasn't her only victim. She was a magpie and stole from friends. sister's friends, from school, from chops - anywhere and everywhere, really. It didn't come to light because no-one wanted to make an open accusation - thief is a horrible label to give a child. She and her sisters eventually just didn't get asked anywhere, and no-one asked them to their homes.
She was a very unhappy child, but she wasn't my responsibility. She got pregnant at 15. Don't know what's happening with there now.
*TBH if something cheap had disappeared in my house, I would have apologised (if appropriate) and replaced it.