Asset Market Effects on Balance Sheets
The textbook assumes that assets are real assets (inventory, equipment, etc.) that are falling in nominal value along with the price level. However, this will not be the case for financial firms, as their assets are almost always fixed nominal loans. So there is an embedded assumption that this only refers to non-financial firms, which is not specified in the quote provided. (Note that “borrowers” does not imply non-financial, since financial firms are major borrowers.)

However, this is a questionable reason to explain a financial crsis. No firm revalues assets or liabilities based on changes to the price level. The real concern is that falling prices imply falling nominal revenues, which are matched against fixed nominal debt payments. So it’s not really the balance sheet value, rather the prospective value based on future profits that are shrinking. In other words, the problem shows up in the income statement, not the balance sheet.

On paper, accounting values are supposed to reflect prospective profits, but in practice, continuous revaluations are not part of accepted accounting procedures. An asset has to be obviously impaired before being written down. Therefore, balance sheet revaluations (other than loan losses) are not the driver of a financial crisis.