Dear Yasmin,
There are two possibilities. First one is that her demand could be genuine. But then what reason has she quoted for her leave? A career conscious person will never do things like this. Therefore, genuineness of the reasons need to be investigated. The second possibility is that she could be taking your company for the ride. She might have some job at hand and she is trying out there. If the things go in her favour then well and good otherwise your company's job always at her hand. Though this possibility is remote it cannot be ruled out per se.
If you have interest then tell your security officer to keep her under surveillance. Let him loiter near her home and check whether in the morning time the lady goes to some office. Generally employees leave for their office between 0800 and 0900 hours. He can do this for 1-2 days. However, if you feel that this is unnecessary then you may just give a call for being absent from her duties without authorisation and if she fails to report for the duty then her name will be removed from the rolls of the company.
There is nothing like withdrawal of the offer. On receipt of offer for employment, the lady reported on the specified day. Therefore, that day onward she has become your employee. If you have not issued her appointment letter then there is no employer-employee relationship and just show in your attendance records that she was casual employee for the day.
One more thing that comes to mind is that the woman employee came to the office on the day on which she was required to but stopped coming for duty next day onward. Therefore, the case merits investigation whether any hesitation holding her back. Just check whether her first day was normal or lady felt that she could be incompatible with the organisation's culture. It could be because instance like someone being brusque with her or HOD's shouting on some other member of the department.
Thanks,
Dinesh Divekar