Stock Units in Pre-IPO company

I previously worked for a company that may soon IPO. During my employment I received some Stock Units, these will become vested when the company IPO's. I know these units are generally taxed as income tax and handled through the PAYE system by the company's payroll department. So on the vest date a certain number are sold to cover the tax liability. My question is, what happens if, as in my case you are no longer an employee of the company when the IPO happens? Do you have to file the taxes yourself as separate income, or does my old company still do the reporting and tax withholding as if I was still an employee? I recognize this is a slightly unusual question but the revenue site is not much help and an accountant I reached out to wasn't much use either.

If you have stock units, as opposed to actual stock, the company should sell to cover your tax liability. Their obligation to operate PAYE doesn't cease because you are no longer an employee.
By the way you did well to hold onto stock units after you left the company. Most unexercised share awards typically lapse when a person leaves the employment before vest/exercise.