Contractual Employment and Notice Periods
These days, most jobs are contractual, and as such, a one-month notice from either side for an 11-month contract is mentioned in the appointment letter/contract document.
If the appointment is casual in nature, then no notice is required. As he walked in, so he walks out, and the employee/employer should have no grievance against each other.
If the appointment is for a longer period or the period is not specified, then in case of walking out without notice, the usual action of governing corporate/industrial/labor rules applies. The pay for the period of no work during the notice period is deducted from his last salary, and other deductions/insurance/deposits can be made without any problem.
Generally speaking, the employer's/employee's good relationship and HR personnel can sort out any such issue. One should always avoid harassment/legal actions unless it becomes necessary. There should be no ego problem. The employer should appreciate the employee's contribution as long as he worked, and after his departure, find a better incumbent. Communication, preferably written, may be served but not pursued. Let the employee find his way and the employer his own. No corporate relationship is permanent or congenial all the time. It, like life itself, has its own pattern and parameters; respect the basic human relationship as supreme.
Regards,
IKMASIH