BUG: Unable to open Stata 118 or 119 format files saved in big-endian… (#58640)

* BUG: Unable to open Stata 118 or 119 format files saved in big-endian format that contain strL data

* Rename test functions to make their purpose clearer

Author: cmjcharlton

doc/source/whatsnew/v3.0.0.rst

@@ -546,6 +546,7 @@ I/O
 - Bug in :meth:`DataFrame.to_excel` when writing empty :class:`DataFrame` with :class:`MultiIndex` on both axes (:issue:`57696`)
 - Bug in :meth:`DataFrame.to_string` that raised ``StopIteration`` with nested DataFrames. (:issue:`16098`)
 - Bug in :meth:`read_csv` raising ``TypeError`` when ``index_col`` is specified and ``na_values`` is a dict containing the key ``None``. (:issue:`57547`)
+- Bug in :meth:`read_stata` raising ``KeyError`` when input file is stored in big-endian format and contains strL data. (:issue:`58638`)
 
 Period
 ^^^^^^

pandas/io/stata.py

@@ -1600,14 +1600,13 @@ def _read_strls(self) -> None:
                 v_o = self._read_uint64()
             else:
                 buf = self._path_or_buf.read(12)
-                # Only tested on little endian file on little endian machine.
+                # Only tested on little endian machine.
                 v_size = 2 if self._format_version == 118 else 3
                 if self._byteorder == "<":
                     buf = buf[0:v_size] + buf[4 : (12 - v_size)]
                 else:
-                    # This path may not be correct, impossible to test
-                    buf = buf[0:v_size] + buf[(4 + v_size) :]
-                v_o = struct.unpack("Q", buf)[0]
+                    buf = buf[4 - v_size : 4] + buf[(4 + v_size) :]
+                v_o = struct.unpack(f"{self._byteorder}Q", buf)[0]
             typ = self._read_uint8()
             length = self._read_uint32()
             va = self._path_or_buf.read(length)