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(* Mein Code *)
var
  InFileName, 
  OutFileName: String;
  InStream,
  OutStream: TMemoryStream;
  ZStream  : TZDecompressionStream;
  [...]

begin
  [...]
  // Zip-Datei laden, maximal 4MB
  InStream.LoadFromFile(InFileName);
  
  ZStream := TZDecompressionStream.Create(InStream);

  // *) Ab hier kommen die Fehler
  OutStream.CopyFrom(ZStream, 0);  // oder auch andere Werte
  OutStream.SaveToFile(OutFileName)
end;

initialization
  InStream  := TMemoryStream.Create;
  OutStream := TMemoryStream.Create;

finalization
  FreeAndNil(InStream)
  FreeAndNil(OutStream)                    

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(* Original Code *)
  [...]
  InputFileName := 'c:\image.png.bzip';
  OutputFilename := 'c:\image2.png'; //rename to original into final code
  InputStream := TFileStream.Create(InputFileName, fmOpenRead);
  OutputStream := TFileStream.Create(OutputFileName, fmCreate);
  DecompressionStream := TZDecompressionStream.Create(InputStream);
  OutputStream.CopyFrom(DecompressionStream, 0);
  DecompressionStream.Free;
  OutputStream.Free;
  InputStream.Free;
 [..]                    

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procedure ExpandStream(inStream, outStream :TStream);
const
 BufferSize = 4096;
var
 Count: Integer;
 ZStream: TZDecompressionStream;
 Buffer: array[0..BufferSize-1] of Byte;
begin
 ZStream := TZDecompressionStream.Create(InStream);
 try
   while True do
     begin
       Count := ZStream.Read(Buffer, BufferSize);
       if Count <> 0 then OutStream.WriteBuffer(Buffer, Count) else Break;
     end;
 finally
   ZStream.Free;
 end;
end;