The things that show up on credit are lates, defaults and how much of your available credit you’ve used.
If you renegotiate your loan with your lender, technically you should get a new Note (spelling out new terms, payments and balance) and your old loan arrangment should be gone.
However, if the bank wants to write-off the lost $100K on their tax return, they’ll likely send you a 1099 and it gets reported as bad debt (they were unable to collect) and they can still report this on your credit as a collection (as in a foreclosure).
If they send you a 1099-C, then they report it as bad debt, forgiven. Which means they won’t go after you anymore, ever. It’s still income to you, but the account on your credit will say, “paid in full” or “account closed,” which is not a negative mark on your credit.