I have been asked on a number of occasions what an employer can do if their employee does not work out their full notice period.
Whilst it can place a small business in a tricky position, rather than insisting that the employee has to work their notice period this can turn out to be counterproductive, with the employee either phoning in sick or being unproductive whilst at work.
You could consider legal action, but this may be time consuming and expensive, so where possible try to find a compromise. If the employee is prepared to work part of their notice period but wishes to bring forward their termination date, ask the employee to sign an agreement to this effect so that no claim can be made at a later date for unpaid wages.
If the employee is off sick during their notice period, manage this period of absence as you would for an employee who has not resigned, apply the same sickness payment terms (statutory or contractual).