As mentioned in Bug 59673, HSSFWorkbook#setSheetOrder is passing internal sheet
indexes in to FormulaShifter's constructor, but these numbers are used to
update the indices of referenced external sheet records. This can corrupt
references to sheets when the EXTERNSHEET records do not exactly correspond
with the internal sheets, such as if there has been a multiple-sheet range.

For example:

===========
import org.apache.poi.hssf.usermodel.HSSFSheet;
import org.apache.poi.hssf.usermodel.HSSFWorkbook;
import org.apache.poi.hssf.usermodel.HSSFCell;

public class MakeBad {

  public static void main(String ... args) throws Exception {
    HSSFWorkbook workbook = new HSSFWorkbook();
    HSSFSheet originalA = workbook.createSheet("A");
    workbook.createSheet("B");
    workbook.createSheet("C");

    originalA.createRow(0).createCell(0).setCellFormula("SUM(B:C!A1:B5)");

    workbook.removeSheetAt(0);

    HSSFSheet newA = workbook.createSheet("A");

    HSSFCell cell = newA.createRow(0).createCell(0);
    cell.setCellFormula("C!A2");
    System.out.println("Before sheet move:");
    System.out.println("  cell formula=" + cell.getCellFormula());
    describeExternalIndices(workbook);

    workbook.setSheetOrder("A", 1);

    System.out.println("After sheet move:");
    System.out.println("  cell formula=" + cell.getCellFormula());
    describeExternalIndices(workbook);
  }

  private static void describeExternalIndices(HSSFWorkbook workbook) {
      System.out.printf("  Sheet %s has internal index %d and external index %d%n", workbook.getSheetName(i), i, workbook.getExternalSheetIndex(i));
    }
  }
}
===========

outputs

===========
Before sheet move:
  cell formula=C!A2
  Sheet B has internal index 0 and external index 1
  Sheet C has internal index 1 and external index 2
  Sheet A has internal index 2 and external index 4
After sheet move:
  cell formula=B!A2
  Sheet B has internal index 0 and external index 1
  Sheet A has internal index 1 and external index 2
  Sheet C has internal index 2 and external index 4
===========

This is because the external index in the formula before the move (2) is the
same as the internal index (1) of the moved sheet, so
FormulaShifter#adjustPtgDueToSheetMove has changed the external index to match
the new internal index of the moved sheet (1). Note also that the external
index records have not been reordered or changed, so the mapping of internal
index to external index remains unchanged.

I think the way to fix this is to change how sheet reorders are handled just in
the case that the external index records are not just the trivial n ascending
internal indexes. When this happens, it is not possible to correct the
references by updating all the Area/Ref3DPtgs as the records for multiple sheet
ranges would be pointing at the wrong set of sheets. Instead, rather than
updating those indices, the external sheet records would need updating with the
new internal sheet ids.

While this approach could also be followed in the case that the external index
records are the trivial case, that would result in the indices getting out of
sync under circumstances that currently both POI and popular spreadsheet
software does not do so.

A complication here is that such a sheet reorder can change the meaning of a
reference. For example, consider a workbook with sheets A, B, and C in that
order, with a formula "=SUM(A:B!A1:B5)" on C. Moving sheet C between A and B
will result in that range including C, while previously it did not. However, I
think this would be the least surprising behaviour POI could have in this case,
as it would maintain the text of the cell formula unchanged. This is also the
behaviour of a couple of common spreadsheet programs that I have checked while
investigating this.