Process Stability is the attribute of a process to perform consistently within the control limits. And a process is said to be capable when it starts delivering as per the customer specifications.
A stable and Capable process is suddenly rendered as incapable when there is a sudden change to the specifications. For example, Car Companies producing Cars on EURO 4 standard are suddenly without a lead time asked to adhere to EURO 5 Specifications. In such a scenario, their process capability exhibits a downward trend and process becomes incapable.