No, you don't need a second passport if you retire, work, or live abroad. There is a misconception people have that they need to either give up their US passport or US citizenship but no, you don’t need to. You can have your US passport.
As Americans, we're lucky that we come from a country where we don't really need to apply for even a visa to visit most countries. We can go with our passport. We can usually stay in countries anywhere from 1 to 6 months, depending on the regulations of each country. In Mexico, for example, we can stay up to 180 days with a US passport.
A lot of people who move abroad still want to go home once or twice a year and visit their family. You might be living in Nicaragua and stay 90 days before re-entering, because, without a visa, you have to leave and come back in. If you live in Nicaragua, maybe you want to go to Costa Rica or take a flight to Colombia. That’s basically what people do. They leave once or twice a year. They either travel around or go back to the US. You can do that all with your US passport. There's no need to make any changes. Just make sure that your passport is valid for a long time so that you don't have to go get a new one. Even if you lose your passport or you need to get a new passport, you usually can do so at the consulate in that country. It's not a big deal. Also, if you're planning on traveling a lot, you can order passports now that have extra pages that should last you a long time or you can get pages added to them about $80.
You can choose to continue doing this indefinitely in many countries. What you decide to do depends on the situation and the residency attorney could tell you about that. It could be expensive to get residency. It just depends on the country. For example, the cost of getting residency in Nicaragua is a fraction of the cost of getting a residency in the UK or in some places in the Caribbean where it can cost over a million dollars. In some countries, it costs a few hundred thousand. In Nicaragua, in Mexico or generally in Latin America, it's always going to be a lot lower, for the most part under $10,000. That might be the route that you take but even if you do that, that doesn’t mean you're going to get a passport from the country that you have residency in. You'll still be traveling on your US passport.
If, for example, you travel to Nicaragua on your US passport and then you want to get a permanent residency or temporary residency in Nicaragua, it could be up to 5 years. You'll still use your US passport to travel. The only time you would need to actually get a second passport would be if you obtain citizenship in that country, which can take 10 to 20 years. You won't really need your second passport under most any circumstances especially if you have a US passport. I can't think of any reason why you would need a second passport. It would be a luxury to have a second one but it's not a requirement by any means.