Eric said:
Is it possible to lock the border formats on a spreadsheet so that they do
not change during cut and paste or drop and drag operations?
No. Formats such as borders are tied to the cell. Cut and Paste (or drag and
drop) involves moving cells, so this inevitably means moving borders with
them.
You can use Copy and Paste Special > Values (instead of Cut and Paste), as
this will paste only the cell contents, not the cells themselves.