A nickel reappears.

401(k) Plan is terminated.  All plan assets are paid out, a final 5500-S/F is filed and the company is sold.

One individual's brokerage account was paid out in a check for $10,000 in March, then a check for 5¢ in April.  The $10,000 is deposited; the 5¢ check goes stale and returns to the account.  Participant can't be bothered to deal with the 5¢ check.  What to do....?

What kind of account are you dealing with?  Just tell them to close the account and keep the 5 cents, or asses 5 cents in fees.  its a rounding error, no one is going to give you a hard time about 5 cents. 

If I had a nickel for every $.05 check I received over the years ...... 

Have the brokerage close the account, tape a nickel to a letter and send to the participant, like various charities do. They've already spent far more in accounting for this already. As an old acquaintance used to say all the time, "there ought to be a law..." - and in this case that any amounts under $5 left in closed out accounts may be forfeited to the custodian and used to defray expenses.