Dear Yasmin,
There are two possibilities. The 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, the genuineness of the reasons needs to be investigated. The second possibility is that she could be taking your company for a ride. She might have some job at hand, and she is trying out there. If things go in her favor, 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 an interest, then tell your security officer to keep her under surveillance. Let him loiter near her home and check whether in the morning, 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 authorization, 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 a withdrawal of the offer. On receipt of an offer for employment, the lady reported on the specified day. Therefore, from that day onward, she has become your employee. If you have not issued her an appointment letter, then there is no employer-employee relationship, and just show in your attendance records that she was a 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 the next day onward. Therefore, the case merits investigation whether any hesitation is holding her back. Just check whether her first day was normal or the lady felt that she could be incompatible with the organization's culture. It could be because of instances like someone being brusque with her or the HOD's shouting at some other member of the department.
Thanks,
Dinesh Divekar