Seems I'm wrong. They must have built up a stockpile, because the factory that made the TA engines switched over to building the new three- and four- cylinder 1.0 and 1.3 "FireFly" engines in late 2018. But the MultiAir technology is still used across the FIAT petrol engine family - the 2.0 litre petrol in the Alfa Romeo Giulia and Stelvio is a MultiAir engine, as are the 1.0 and 1.3 turbos used in Jeep and FIAT small SUVs. Its big advantage is that it lets you get high performance out of an engine without making it undriveable or grossly inefficient at low speeds. For the 500 and Panda, the performance of the new 1.0 engine is perfectly fine, especially with a bit of mild-hybrid assistance off the line, so there's no need for MultiAir.
It's not a direct copy of the original 500 engine, but it is, like that one, a twin-cylinder. It was developed as a demonstration of the MultiAir system, and also with a future hybrid car designs in mind. In the end, for other reasons (FIAT taking on Chrysler in 2009) those plans were mothballed.
Yes.. FIRE stands for "Fully Integrated Robotized Engine", and is indeed a descendant of the original 1985 model - the first car engine to be fully assembled by robots. It's later than the FIAT Ritmo (Strada in UK), which was the car advertised as "handbuilt by robots", a really big deal in 1978.
Fiat Strada - "Handbuilt by Robots" - YouTube
FIAT was a pioneer of automated assembly - some of the other futuristic ideas in that factory included the automatically-guided vehicles that bring bodies and components between stations (you can see them in the ad); the technology of the time meant that it turned out to be less reliable than conveyors and guys with carts, but the idea itself was sound, and in the most modern car factories you see AGVs with adjustable height platforms on them bringing cars from station to station - this time they're guided by radio-location, not optical tracks.
The FIRE engine family was finally retired in 2020 - it's been replaced by the 1.0 and 1.3 litre versions of the new "FireFly" engine family, with or without MultiAir and/or turbocharger.