As far as I know there is no legal impediment to offering a salary advance. Some councils strictly forbid it, whilst others only allow it under exceptional circumstances and with limits on the amount offered.
As Graeme-r has already said - a job for the full council in the end.
However, I think I would want to know more about the circumstances - is this a truly one off problem or is there some other deeper problem in the offing. How will the advance be repaid and over what period? I can imagine a situation where the lower income on the next payday may in fact exacerbate the problem. What will the position of the council be if the employee suddenly left the council after the advance?
The staffing committee perhaps ought to make some discrete inquiries and report to main council in confidential session.