The Passport is one of the most sought after documents in South America. A stolen then altered passport is worth thousands of dollars on the black market.
When you arrive in Ecuador, you should make several color copies of your passport. Carry those with you and not your original passport. Have the color copies notarized by a Notaorio, then give a notarized, color copies to your lawyer, an official and to customs when requested -- do not give anyone your original passport. Put your original passport in the safe at your hotel. If there isn't a safe then hide the passport -- do not leave it where it is easy to find.
For example, when you take your passport to an official, take a notarized, color copy. Show the official that they are identical and leave the color copy with them. One of the leading law firms in Cuenca explained that there is no requirement to leave your original passport with any official. One story that a lawyer at this firm told me was of an expat who sent his passport to the lawyer he was using -- only to have that lawyer disconnect his phone and move his office. The man could not find the lawyer or the passport.
Loosing your passport in any foreign country is sticky matter, so do you best to know where your passport is at all time. One or two back up copies is some safe guard.
Also do not carry you wallet or purse with you with all of your identification and credit cards. Carry one or maybe two cards with you and a color copy of your passport. Keep each card in a different pocket. Keep your money in different pockets as well. If something happens, maybe you'll only have to give them part of your money.
Be careful and have a good experience.
For more information or questions write RelocationServicesEcuador@gmail.com