In this particular case the woman claimed that she did not know herself that she was pregnant at the time she left and as such could not inform you. HMRC would accept this as a valid excuse and so the payment is due. However, you can console yourself with the fact that as a small employer, you can recover the full amount from HMRC.
Whosoever employs the worker at the end of the tax year will produce the P60.
Remember, a P60 will show earnings from the previous employment (information passed via the P45) and earnings from the current employment; thus covering the whole tax year in the one document.
If an employee has no employment at the end of the tax year, they will not receive a P60 from any employer and the P45(s) will contain all their earnings history.