This is an interesting question because the answer, in relation to historic periods, is it depends.
The employer has an obligation to deduct the correct PAYE/PRSI etc from the emoluments paid to the employee, and in any event to remit the correct amount. So they are on the hook for the incorrect deduction.
In theory Revenue could also revisit the balancing statement / assessment of the employee to recoup the tax from them but in practice they generally tend to only address issues with incorrect payroll deductions, with the party whose error it was to not operate the tax correctly, namely the employer.
If they believe that the two parties were colluding in order to pay inflated tax free expenses as a form of wage substitution, then they could pursue both parties - the employer for the tax which ought to have been deducted but wasn't, and separately the employee by way of assessing them for the correct amount of gross earnings (but without credit for the additional tax paid over by the employer, as it was not deducted from / borne by the employee). The effect of this would be similar to grossing up the net amount of expense paid, where the additional tax cost is shared between the two parties.
With effect from the beginning of this year, the employer bears the responsibility now, and the amount overpaid would be liable to tax / PRSI etc on a re-grossed basis, under the new PAYE rules.