Settle up on the People tab handles the ending.

They paid me / I paid them — logs a real entry that draws the balance toward zero.
Let it go — you forgive what they owed. That money truly left you, so it becomes your spending (a treat you gave).
They shouldered it — they covered you for good. Nothing ever left your accounts, so nothing is counted.
I kept it — they told you to keep their money, so it becomes your income.

Every option takes an amount and a date, so you can settle just part of what's owed and leave the rest. Each entry in a person's history also has its own small Settle button, which fills in that item's amount — handy when someone owes you for two separate things and you only want to close one.

Fronted, then treated them anyway? Log the entry at its real full amount, name them as they owe me for their share, then later hit Let it go. You keep the whole story, and the forgiven share correctly lands back in your own spending.

IOUs. If a friend pays the merchant for your share, no money leaves your accounts — so there's no entry to name them on. That's the one case for a standalone IOU on the People tab. Pay it back later and the balance clears.

Flat entry, or name someone? Both give the same balances and the same stats, so it comes down to what you want the ledger to show. The question: could one half happen and the other fail, or be forgotten? If it completes as a single exchange, log it flat. If the two halves are separate acts — you fronted something, or you're holding their money until you can pass it on — name them, so the debt stays visible for its whole life. It isn't about elapsed minutes, it's about exposure: did you have to remember anything afterwards?

Money that's just passing through. Only what sticks to you counts. Acting as a human ATM (someone hands you cash as you send them the same amount) is a transfer, not a debt — nothing is owed once it's done. A fee is yours only when it leaves your account; a commission you earn is income. And if someone's money lands in one account but you spend it from another, name them on those entries as their money — your balances stay right and your stats stay clean.