Correcting Participant who elected 10% pre-tax but deferred Roth

Participant elected 10% pre-tax for all of 23'. Issue with payroll caused this person to defer 10% Roth instead.  Correcting this sounds messy (new w-2, moving buckets of money, etc.)  My idea is to tell the sponsor to shore them up via payroll with the extra taxes they had to pay. They then get tax free growth for essentially "free".  What else am I missing besides the fact that they couldn't defer paying taxes until later in life?

I don't know what this means: "Issue with payroll caused this person to defer 10% Roth instead." Do you have a failure to comply with plan terms if regular deferrals were elected and instead Roth is credited? Your solution might make the participant happy enough, economically, if you did a full gross up (calculate it before you suggests it), but what about compliance?

I agree with QDROphile.  There is a Plan operational failure because the Plan did not carry out the participant's election as they requested (presumably the election was in accordance with plan terms, etc.).  The contributed amounts, though the same dollars in the Plan, should be characterized as pre-tax and not as Roth.  It is not up to the plan to make that decision.  The participant did not "designate" those contributions as Roth contributions and so they should not be characterized as Roth contributions.  I agree that from a practical and personal tax standpoint grossing the participant up for the taxes sounds great (biggest "mess" to me is that with the amended W-2 comes an amended 1040 and potential penalties on the participant) but, again, this does not resolve the Plan compliance issue.  If this was VCP mayyybeee this correction would be okay if floated to the IRS, but this appears to be a non-correction/self-correction that does not comport with the self-correction guidelines.  Also, not sure what's the "issue with payroll caused" but could this have happened with anyone else??