Liz Buchanan BVSc MRCVS
That looks to be under the forelimb and there are a few possibilities. It could be an abscess, a walled-off ball of infection introduced by a bite-wound or other dirty penetrating injury. I can't rule out a an over-licked skin problem, foreign body or cancer of the lymph-node bursting out. At its most benign, this hole will merit treatment - cat-appropriate pain releif if nothing else (NEVER human pain meds), and perhaps some physical way of stopping the licking. This should be prescribed by a vet who can assess the patient in context. Please will you let us know how you get on?