The IRD will not accept negative values in pays sent to them via payday filing. What to do next depends on the reason for the negative amount.
Mistake in pay
A common reason for negative pays is simply that there was an error in the pay. Perhaps the employee had a fixed deduction in their pay but didn't earn enough this week to cover the deduction amount. If the pay was in error, simply remove the employee from the Pay Run or amend the inaccurate pay line.
Negative amount for final pay
If an employee has taken more leave than they had available and is now finishing as an employee, they may be owing you some money.
The way to handle this will depend on whether the employee will actually be paying you back the amount owing.
If you don't intend to recoup the amount then simply don't do a final pay for them. To achieve this you'll need to edit the employee and put a finish date against them. Depending on the dates they may be added to your next pay as a Final Pay - simply remove them from the pay and proceed as usual. The negative balance will be retained which is a correct representation of the state when the employment finished.
If you intend to get money back from the employee then the final pay needs to be incorporated in the last pay when they had earnings to cover the amount being paid back. Rather than doing a single negative pay as the final pay, mark the previous pay as a draft and set that as the employee's Final Pay. Resend that pay. The difference between the take home pay in the newly processed pay and the original pay is the amount you will be wanting to recoup from the employee. This will have correctly adjusted the tax amounts for the difference which won't happen if you process the negative pay in isolation.
Information on marking the previous pay as a draft can be found here: Fixing a Mistake in a Sent Pay
Over-payment in a previous pay
If the over-payment was in a previous pay, the easiest way to adjust for it is to edit a sent pay. Select Mark as Draft on the previous pay, amend it with the correct values, then resend the pay. The difference in take home pay between the original pay and the re-created pay is the amount the employee will owe you. This can be put into a subsequent pay as a post tax deduction. Resending the pay will file an amendment.
If you really want to enter a negative pay then you will need to use myIR to manually adjust the returns for the employee. In myIR you can edit previously returned files. If the adjustment is for a period before the current tax period it might be worth contacting the IRD to discuss.