If a bank fails, will debt be wiped out?

No, your debt is an asset. In bankruptcy assets might be sold off (there are different flavors of bankruptcy and they don't all involve complete asset liquidation). Your debt would either remain with them or be sold to another company.

Absolutely not. Herstatt Bank went bankrupt in 1974. It took them about 20 years to collect all outstanding debt (bank going bankrupt when you have a 20 year loan means you still have 20 years to pay it back), with the result that the bank fulfilled 97% of its financial obligations, but it took twenty years.

Statute of limitations doesn’t matter. If you take a 30 year mortgage there is no statute of limitations that allows you to stop paying. Whether the bank is solvent or not.

The bank MUST sell your debt to someone else. It must because it is obliged to sell off its assets (your note) to satisfy its creditors.

The bank is not free to just leave your debt lying around in its inventory, going "la la la, I think I'll just leave these debts sit here unattended". The landlord, the county tax assessor, OfficeMax, the Acme Safe Company, etc. etc. are banging on their door going "Pay me!"

Once it's in bankruptcy, this is even more certain, since bankruptcy is essentially court oversight of the sell-off. So they MUST provide complete records and satisfactory answers to the court, and the creditors are watching like a hawk.

There is no way a file drawer full of mortgages are going to get "forgotten about". Let alone a computer full.

As R. Hamilton notes, a few got lucky in the mortgage bust in the 2010s, but that was more about punishing creditors for being careless and lying. That's not something you can take... to the bank...

This can unintentionally happen.

As the other answers have pointed out, what happens in bankruptcy (chapter 7 to be specific) is that another company buys the debt and life continues as normal for the debtor. From the debtors perspective it is no different than a solvent company selling off their debt to other companies, which happens all the time (particularly with mortgages and car loans). You might get your car loan from GM financial, and they might sell the loan to another company, but you still have to pay the loan.

But it is possible that in the shuffle the proof that you owe the money is lost:

https://www.nytimes.com/2017/07/17/business/dealbook/student-loan-debt-collection.html

Judges have already dismissed dozens of lawsuits against former students, essentially wiping out their debt, because documents proving who owns the loans are missing. A review of court records by The New York Times shows that many other collection cases are deeply flawed, with incomplete ownership records and mass-produced documentation.

While the article is about student loans in particular, other forms of debt have been wiped away in this manner. As I recall there were articles about this sort of thing in the aftermath of the 08 financial collapse, where some people's credit card debt was eliminated because the paperwork was lost.

No

You would still owe whoever gets the banks assets.