Employee eligible to participate in 401(k) completed all appropriate enrollment forms to defer 5%. However, employer never set up in payroll and employee deferrals were never withheld/deposited.

What are the correction issues if the employee refuses to "pay back" lost deferrals? If the employees pays back lost deferrals?

If possible, please provide reference. Thanks.

I would not make the employee liable for paying back the deferrals but would treat this like an eligible employee who was treated as ineligible by mistake. The employer should make up the deferrals, any corresponding match and also reasonable market gains. See Rev Proc 2003-44 Appendix A, Sec. .05.

You did not specify how long it took to discover the oversite. The reason this is important is Rev Proc 2003-44 Appendix B, Section .02 (1)(ii)(E) provides that no make up contribution for deferrals is required if the employee was able to participate for at least 9 months in the plan year. However, if there were matching contributions, those would have to be made up. See Example 7 in the Rev proc.