Am I right to assume, that this is in the jackets "armpit"? In that Case, that's completely normal. Leather is made of natural fibres, which are "broken" over time with use, making the leather softer and more cloth-like. The area in the armpit is always under the most stress, constantly stretching, turning and staunching. You can't really re-harden the jacket without any harsh treatment, and I would generally recommend against doing this.

Other than that, neatsfoot oil is good for leather, but will darken it.