Well what process does your nation have, wherever you are from? I just never thought that a country would not allow one to renew their passport at their respective Embassy or Consulate. What do your people do, that it sounds like such a strange idea to you?
Also, if you are a foreigner, in Mexico, why are you on this forum???
I am Canadian. The Canadian process for renewing an expired passport while abroad is very similar to the American process. So the idea of renewing an expired passport at a Canadian embassy or Consulate is not so strange to me. In fact, I recently underwent this process and am therefore quite familiar with it. I also have many American friends here in Mexico, and they go through the American process all the time.
While I am pretty up-to-date on the American and Canadian processes involved in renewing expired passports while abroad, I have no information regarding how Mexicans can do this. The Mexican process may be similar to the American and Canadian processes, or it may not. Whatever it is, I believe it is quite irrelevant to your situation. However, if my belief is incorrect, can you please explain how knowing about Mexican passport renewal processes will help you?
Finally, I am on this forum because I have knowledge about American expired passport renewal processes while abroad. These forums do not require that participants actually live in the US (if that were the case, you would not be allowed here either), only that we have enough relevant knowledge to answer questions. I do.