There's no sympathy required here.
The process is that the employer, making a payment of emoluments in 2017 is obliged to operate PAYE on it in the normal way. That's how the PAYE system works - it's a system for collecting tax, not a system of assessing individuals' final tax liabilities.
The individual themselves is chargeable to income tax on emoluments by reference to the year the income relates to. This is an established principle of tax law and there is case law to that effect dating back to the early 20th century.
So as Mathepac said, the individual needs confirmation from HR in their department of the make up of the back pay; they can furnish this to Revenue with a request for all affected years to be reviewed and the 10k of income appropriately spread across the years.
What should happen is that they will have underpaid tax for all back years (as their taxable income will increase for every prior year) and they will have a substantial overpayment of tax for the current year. If they were a standard rate taxpayer in the earlier years they may get a good chunk of the tax that has been deducted back. If they weren't, then it may not make much difference.
The position with regard to USC/PRSI is different AFAIK as these are due by reference to the payment itself rather than the period that the payment actually relates to. However, this may work out in the individual's favour as rates of income levy / USC were higher for the last 8-9 years than they are in 2017.
I'm not sure what the position is with the PRD, but that's not a tax, it's a deduction from pay. But it needs to be considered.
It may be worthwhile for this person to engage a tax advisor well versed in this type of issue to deal with it and to check the numbers, because if they are suffering more taxation than they otherwise would have, and it's a material amount in the difference, they should probably be seeking further compensation from their employer to make good their net position.
Also, as the back years all need to be opened up so as to account for additional income, the individual should ensure that at the same time they claim any and all previously unclaimed tax credits / reliefs.