My last paycheck as an employee was paid in early January but my last day was 12-31. The former employer contributed in error to my 401k for the new year with my money earned in the previous year. They are now saying that I actively participated in their retirement plan on my W- 2 which could make my IRA contribution nondeductible. They won't change it even though they are wrong in my opinion and that I should have brought this to their attention when it was paid. Unfortunately we did not catch their error but we still did not willingly participate and we were not employed.
The vast majority of individual taxpayers in the United States operate on a cash basis of accounting. This means that the assignment of deductions or income to tax year is based on the date of the paycheck. So the money in that early January 2016 paycheck has been correctly assigned to the 2016 tax year.
This is unfortunate for you because you will receive a W-2 for 2016 showing that you had a retirement account.
Knowing exactly how many paychecks there are in a year can be very import to know when trying the reach or avoid some thresholds.
Even quitting the previous pay period might not have helped. I have seen some companies payout unused vacation, sick and severance over several paychecks. They didn't give you it all in one lump sum, they did it 80 hours a paycheck until the balance owed to the employee was zero.
Publication 590a covers this in a fairly specific manner.
Page 11, section "Are You Covered by an Employer Plan?", specifies:
The Form W-2 you receive from your employer has a box used to indicate whether you were covered for the year. The “Retirement Plan” box should be checked if you were covered.
So, by default, if that's checked, you're covered. 590 does go into more detail, though.
Assuming you're covered under a Defined Contribution plan (a 401k for example):
Defined contribution plan. Generally, you are covered by a defined contribution plan for a tax year if amounts are contributed or allocated to your account for the plan year that ends with or within that tax year.
Tax year. Your tax year is the annual accounting period you use to keep records and report income and expenses on your income tax return. For almost all people, the tax year is the calendar year.
Further, they cover issues related to an employee leaving Dec. 31 very specifically:
A special rule applies to certain plans in which it is not possible to determine if an amount will be contributed to your account for a given plan year. If, for a plan year, no amounts have been allocated to your account that are attributable to employer contributions, employee contributions, or forfeitures, by the last day of the plan year, and contributions are discretionary for the plan year, you are not covered for the tax year in which the plan year ends. If, after the plan year ends, the employer makes a contribution for that plan year, you are covered for the tax year in which the contribution is made.
Example. Mickey was covered by a profit-sharing plan and left the company on December 31, 2014. The plan year runs from July 1 to June 30. Under the terms of the plan, employer contributions do not have to be made, but if they are made, they are contributed to the plan before the due date for filing the company's tax return. Such contributions are allocated as of the last day of the plan year, and allocations are made to the accounts of individuals who have any service during the plan year. As of June 30, 2015, no contributions were made that were allocated to the June 30, 2015, plan year, and no forfeitures had been allocated within the plan year. In addition, as of that date, the company was not obligated to make a contribution for such plan year and it was impossible to determine whether or not a contribution would be made for the plan year. On December 31, 2015, the company decided to contribute to the plan for the plan year ending June 30, 2015. That contribution was made on February 15, 2016. Mickey is an active participant in the plan for his 2016 tax year but not for his 2015 tax year.
Mickey is in a similar (but different) circumstance, and it's clear from the IRS's treatment of his circumstance that you would be in the same boat (just a year less off) - but be aware given Mickey's situation that it's theoretically possible for them to make another contribution next year, as Mickey had, depending on when their plan year/etc. ends.
So - from the IRS's point of view, everything you said the company did is correct. They paid you in January, contributed to your 401k as a result of that paycheck, and thus you were officially considered covered for 2015.
According to the IRS, you can still put money in your IRA. Here (https://www.irs.gov/Retirement-Plans/Plan-Participant,-Employee/Retirement-Topics-IRA-Contribution-Limits) they say:
Can I contribute to an IRA if I participate in a retirement plan at work? You can contribute to a traditional or Roth IRA whether or not you participate in another retirement plan through your employer or business. However, you might not be able to deduct all of your traditional IRA contributions if you or your spouse participates in another retirement plan at work. Roth IRA contributions might be limited if your income exceeds a certain level.
In addition, in this link (https://www.irs.gov/Retirement-Plans/IRA-Deduction-Limits), the IRS says:
Retirement plan at work: Your deduction may be limited if you (or your spouse, if you are married) are covered by a retirement plan at work and your income exceeds certain levels.
The word 'covered' should clarify that - you are not covered anymore in that year, you just got a contribution in that year which was triggered by work done in a previous year. You cannot legally be covered in a plan at an employer where you did not work in that year.