Contrary to what some think, employers can take action when an employee is persistently absent through sickness. It is possible to dismiss an employee fairly for reason of absence through sickness ot indeed other reasons that create absence. That said, the employer has to act fairly and give appropriate time for the employee to improve his/her attendance record. The case would depend on individual circumstances and the employer would have to use the written warnings procedure. So if this the first case of absence, then no. If this is the latest in a catalogue of absences for which the employeee has been warned about attendance previously, then it is possible.