If a new employee has signed a letter of employment but does not show up for work, what can an employer do?
Once an employment contract has been signed, both employers and employees should be prepared to fulfil their contractual obligations. In exceptional cases when they are not able to do so, they should inform the other party as soon as possible.

If an employee does not show up on the first day of work, the Employment Act does not apply as the employer-employee relationship has not started.

An employer will not be able to claim notice pay or any other compensation provided for in the Employment Act. They can consider a civil claim filed through their own lawyer.

From MOM website...
Be prepared to get sued. If the company not happy you no show. Then whenever you fill up form you have to legally declare that you are involved in a civil sue. My ex colleague kena sued before when he quit the company to join direct competitor. Its in the contract non compete. But the competitor promised to pay the legal. They paid...

But now he got the black mark in his record that he kena sued before. And legally he paid the fine. Even though that money was paid by the competitor company.

Go ahead do what you want.