Dear Vijay,
When any employee in the organisation is absenting unauthorisedly, you need to send them atleast 2 notices wherein 1st one will ask the explanation for his absence & asking him to resume to duties immediately; The 2nd notice, if he is not responding- your services are terminated from your date of absence & you are not eligible for any kind of benefits which otherwise you were eligible.
If this would have been done, this confusion would have not arised.
Coming to your query--- As that lady has not served the given notice period, such amount can be recovered from her & the remaining amount can be paid in her Full & Final settlement. Issuing relieving order is a secondary question because she has not completed her relieving formalities. She is not relieved officially & you need not give her a relieving order.
Coming to experience letter--- An experience letter is a certificate which is certifying an employee about his/her service in the company. A certificate is issued to employees who has behaved well. The Management must provide it heartfully & not by any force. Management reserves the right to issue it or not.
When it comes to humanitarian grounds, if you are not issuing the relieving order, her future career steps are into trouble. If you are not issuing the experience letter, she cannot show her experience else where & claim more salary. There is a black mark left in her career life at every step. These would be the after effects maximum for this employee.
On these grounds, you can take a proper decision. If you want that employee not to repeat the same else where, donot issue. By this other employees are also taught a lesson. Nobody else would dare to repeat the same. If you donot want the employee to suffer just for this reason, just issue the letters & close the issue silently. You need not keep anything personal with the employee.
Regards,
Bharghavi