The practice you describe sounds like an extension/modification agreement. If that is the case, it is very common practice in many states.
Personally I prefer a thoroughly underwritten new note, but extension/modification agreements are recognized by courts as an effective tool. The extension/modification agreement is a two party agreement and therefore should bear the signature of the bank and the borrower. Seek guidance from your legal counsel on whether an unsigned agreement is enforceable.
Recently some examiners have raised an issue regarding using extension/modification agreements on loans that have already matured, but many banks have successfully followed that practice for many years.
The issues raised in the two prior paragraphs are not a concern when a properly completed new note is used.