First it somewhat depends on how far you have gotten towards filling her position and whether her notice period was over.
If she has already left, she is no longer an employee and deserves no more consideration than any other candidate for the vacancy. in this case:
- If you have interviewed candidates who are stronger than she was,
then tell her that the job is no longer available.
- If you are not sure or very far along in the process, tell her she
can reapply and be interviewed and evaluated with the rest of the
If she is still an employee serving out her notice period, you need to decide if she can take it back depending on several factors:
- In the short time she has been there, how good was her work ethic?
- How well did she mesh with the team?
- Did the skills she actually showed you seem to match up well with the
skills you thought she had from the interviewing process.
- What is the company HR policy and the laws of the country concerning
notice periods. Before you tell her anything, you should consult with
HR as to whether staying is a possibility. I don't know your local
laws, so I don't know how much leeway you have to tell her she has to
go or to let her stay. Your HR should know that though.
- What is your personal judgement of her character? She ran away and
lied in a tough situation. You need to make a determination based on
what you know of this person, if this is a charactor flaw or
something she would only do under intolerable stress. I realize you
can't know her well at this point, but you know her better than any
of us. How stressful is this position, what impact would a person who runs away from stress have on productivity?
- Would her return disrupt the team? Would it create resentment? Would
she have to explain her private circumstances in order to be accepted
again? In particular, this can cause a problem if someone they knew
better and liked was not given this same opportunity to return in the
near past. This is especially true if you fired someone and team
felt it was unjust.
While I feel sympathy for the woman, don't rehire her just based on feeling sympathetic. She made the choice to quit rather than tell you the problem. She has to understand that actions have consequences. If she impressed you enough to keep her and the other factors align, then fine. But if you think she will be a problem, then tell her no. Judgement is part of what you get paid for as a manager. This is a case where you have to exercise it even with less information than you would like. It's a hard choice to say, "No" when someone is in trouble in other parts of their life, but as a manager, you have be willing to make hard choices.
If agree to rehire, then you as a manager need to commit to watching her performance fairly closely the first few months. If you see a pattern of avoidance or lying, you need to take steps to let her go.
My personal feel is that if you strongly wanted to rehire her, you would not have felt the need to ask the question, but only you can answer that.