"Saving" in the accounting identity is just money not spent on consumption. Cheaper imports can increase domestic saving because people now spend less for the same goods. That could then increase domestic investment due to the increased savings.

Or the same situation could reduce savings, if people increasing consumption because the imports are so cheap.

The accounting identity doesn't explain anything other than the mathematical truth that the money needs to add up in the end. Savings are not inherently good, deficits are not inherently bad