"about repayment of loans to deceased TSP participants"

Let's try another perspective:

Two scenarios.

1.

You have an account with $1,000 in it. You ask to borrow $500 from me pointing out you have an account that can secure this loan. Then, you spend all that money and what is in your account and go broke and can never repay me. I forgive your debt to me. Your total of funds available and spent was $1,500: My $500 and your own $1,000. You "made money" and that is why forgiven debt is income to you.

That is Loan Forgiveness. It involved additional funds and that component never gets repaid. You benefit.

2.

You have an account with $1,000 in it and ask me to give you some of it on a temporary basis. You are supposed to be repaying it, and the terms mean we don't consider it a Distribution at that time. But you don't repay it, because you Die.

Your beneficiary is supposed to get your account balance. You didn't take a Distribution as such; you drew against it as a Loan. That's why it was not reported as Distributed yet. $500 was "forwarded" and $500 remains. I issue the reporting for $1,000, but there is only $500 to pay out now, because $500 was paid out earlier. The first payout is just now being reported for purposes of Distribution, because just now is when it is determined (being "declared") there will be no payback of that loan, which really is your own Advance. You borrowed from yourself, so there is no additional amount.

The total involved here is $1,000. It's a timing issue. This is why it is called an Actual Distribution and not a Deemed Distribution in the IRS literature. It is a distribution, but with delayed reporting.

"and the loan of $25,000 was paid off before she got the $5,000 that was left, the kid would have to pay tax on $30,000 income?"

If the loan had been fully repaid to that account, then No. The kid would get $30,000. There would not be only $5,000 left. Remember, you borrow from yourself. The original account holder would not have seen it reported as a Distribution, as long as the repayment process to himself proceeded to completion.

"but maybe I'm not looking in the right place."

From Pub 721, pg 14: "Outstanding loan. If the TSP declares a distribution from your account because money you borrowed hasn't been repaid when you separate from government service, your account is reduced and the amount of the distribution (your unpaid loan balance and any unpaid interest), from traditional contributions and earnings, is taxed in the year declared."

TSP resources:

https://www.tsp.gov/publications/tspbk04.pdf

https://www.doi.gov/sites/doi.gov/files/migrated/flert/training/upload/Withdrawing-Your-TSP-Account-...