The top layer of fur and possibly skin looks to be missing, so infection may also be an issue. I would fully recommend a buster collar, but of course the toe is really itchy (I don't know if you've ever tried not to scratch an itch) so simply preventing licking without treating the toe could be extremely frustrating for its owner.
It sounds as though a vet needs to see this toe pretty soon in order to discuss treatments. Usually, when being licked, such lesions are itchy and uncomfortable, so cancer is much less likely than if it were being ignored. Insect or even cat-bites are not completely impossible, but very uncommon. Allergies can also present like this, if over-licked and swollen. They very rarely present with an obvious entry-hole because often they entered the foot a while ago and can move around once inside rather, the first sign tends to be a swelling from when the body reacts to the foreign body and tries to expel it. Hello! One of the most common reasons for a presentation like this would be a grass-seed (they are torpedo-shaped at both sharp ends) or a similar small foreign body that cuts into the skin between the toes.
