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what if a former employer contributes to my 401k in the year following my exit?
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: 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: 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.