As a former elementary school counselor, I think Jane's behavior is serious. If this were my DD friend, I would keep them apart. Ask the school to change Jane's locker and keep in touch with the teacher, counselor, or principal to make sure there are no continuing problems. I would not allow my DD to be friends with this girl at all, not even at my own home. I would tell DD to quietly say she can't be friends and then not hang out with the girl. Hopefully your DD's other friends will not be friends any longer with her either.
I know this sounds harsh to some people but Jane seems to have serious problems that a professional needs to handle. Keeping your DD away is the best thing you can do. This isn't something kindness from you or your daughter will be able to cure. Have DD invite the other girls over and keep them as a good group that she will be safe with for many years to come. All of them staying away will be best for them. The principal and counselor can recommend help for Jane.
I know this sounds harsh to some people but Jane seems to have serious problems that a professional needs to handle. Keeping your DD away is the best thing you can do. This isn't something kindness from you or your daughter will be able to cure. Have DD invite the other girls over and keep them as a good group that she will be safe with for many years to come. All of them staying away will be best for them. The principal and counselor can recommend help for Jane.