"To repeat: if the chain of title of the note is broken, then the borrower no longer owes any money on the loan."
This is the sort of arrant nonsense that lands the gullible in a heap of trouble. Typically, there are two separate instruments involved when one obtains a loan secured by a mortgage -- the first is the promissory note, which says essentially "I owe Bank X $1000". The second is the mortgage deed, which says essentially "to secure my obligation under the promissory note, I grant a mortgage on my house". Typically, they are both owned by the same party. When things are screwed up, they can become separated.
Hence, one seeking to enforce the promissory note may find they are not the owner of the mortgage deed. The noteholder can remedy the problem through the means suggested above and, once it obtains the mortgage deed, commence a foreclosure. But, importantly, the holder of the defaulted note need not do so. It can instead, commence an ordinary contract action against the borrower and obtain judgment on the note itself. It may then enforce that judgment by executing on any unencumbered property of the borrower. This is not the best result for the lender, but it is possible. Importantly, the borrower always owes the money to the current holder of the note, whoever that may be.* It is dangerous to give people the impression they are off the hook when there is a defect in the chain of title. They are never off the hook.
* Note: this assumes the current holder is the holder in due course. If not, the last legitimate holder in due course can enforce the note. In any event, it will eventually be sorted out and, as noted, the obligation never just disappears.
I still have not seen any proof of this.
