If any employee dose not serve the notice period before leaving the job ,how the employee can take his/her dues ?

Check the labour laws in your area. Without knowing where you are no one can answer your question. In my area (Ontario Canada) an employee must give 2 weeks notice and the employer must give 2 weeks notice as well before laying off. If the employee doesn't they will only get the pay period of the weeks left owing and vacation pay that is owed. Nothing else. If your in the United States it could be different. I would search online for your area's labour laws.

As the previous poster mentioned, a great deal will depend on your location. Additionally, are you a union, contract, or at will employee?

Again it does depend where you are,what your contract states when starting the job.

If you have to work a month in hand then you would be paid that when working your months notice, if you do not work your months notice then you would be paid : hours worked and any holiday that was due to you.

Should you choose to just up and leave then you would be paid only for the hours that you have worked.
The management reserve the right to withhold any holiday pay,for failure to complete your notice.

Casual work( cash in hand )is paid hourly.You are not entitled to any holiday pay.

I am in the UK.

Dues? Are we talking about labor union dues OR salary?