Actually, a lot of companies will stipulate in your contract that you must have a 'satisfactory attendance record' and that if you don't then you could face disciplinary action. If they go down the route of disciplinary action then it could eventually lead to dismissal. A poor attendance record can and would include sick leave.
In practice, if this the sickness is clearly unavoidable (i.e. theyre not skiving) and they have a good record beforehand, then most companies wouldn't take action.
I'm assuming the person has been with the company more than a year and was promoted 4 months ago?