SSP is only payable for 28 weeks in a three year period. Once SSP runs out, you are not obliged to pay any more - unless your contract of employment provides otherwise (see question four). You are, however, still the employer and the contract continues - unless you have decided to terminate the employment, on the grounds of incapacity/sickness. If so, you must follow your normal disciplinary procedures - which must be equivalent to or better than the statutory minimum - warnings, consultation with the employee, obtaining medical evidence, the opportunity for the employee to make representations, the opportunity for the employee to appeal and so on.
An employee who has exhausted his entitlement to SSP may be eligible for incapacity benefit from the State.