Yes, this needs to be reported on your wife's (your joint) tax return.
Codes L1 an 1 indicate that the 401(k) plan has issued a deemed distributions for defaulting on the loan, causing the outstanding loan balance to be taxable and subject an early distribution penalty. A default occurs when the a loan payment is missed and the repayment shortfall is not made up within the grace period, usually 60 days; making up the shortfall after the grace period does not undo the deemed distribution. The taxable amount of the distribution shown in box 2a of the Form 1099-R will be included on Form 1040 line 16b and the 10% early distribution penalty will appear on Form 1040 line 59.
A deemed distribution only makes the loan amount taxable. It does not satisfy the loan, so your wife is still required to pay back the loan. Loan repayments made after the deemed distribution become after-tax basis in her qualified retirement plan. When she eventually receives distributions from the plan, a portion of each distribution will be a nontaxable distribution of her after-tax basis and the remainder of each distribution will be taxable (and potentially subject to an early-distribution penalty). This means that taxes are not paid on the same money twice.
