Though less common in NA vs the rest of the world, CVT have been around for about as long as regular automatics. The ones in the 11th gen Corolla (and some 12th gen variants) are 10 years old (7 years in NA) and build by Aisin-Toyota That says something, since neither Consumer Reports, TrueDelta or JD Power noticed a decline in reliability. You’ll find a couple of blown ones on forums, but nothing out of proportion compared to any regular automatic or other mechanical device. And nothing compare to Nissan-Jatco units that gave the CVT is bad reputation for some.
There was a “service campaign” for a firmware update (2014-2017). Firmware may vary depending on models/areas.
It’s not clear if it was related to the «fake shift points» (and/or the paddle shifting option in some “S”) that Toyota added to mimic a regular automatic so that reviewers wouldn’t be so put off by the way a CVT normally work, without constant rpm variation, which some associate with lesser performance. Actually, the Corolla CVT performs better and smoother than the ones with 4AT (still available in base “L” variant in 2014-2015). Anyway, the issue was premature wear. In actuality, not so many were already affected, in which case Toyota provide repair (valve body control replacement).
Don’t be baffled by posts on forums blaming Toyota for alleging “lifetime fluid”. It’s a urban legend and not what the maintenance schedule says. Recommendation is the same as for any other Toyota automatic transmission: fluid change at 60K (severe service), or when required upon inspection (every 30K). Inspection is visual (for leaks) and data to check if the transmission overheated at some point, which is the first enemy CVT fluid. And CVT are very particular about fluid. It’s the key to longevity and sometimes the “unknown” factor when buying used.
Some models may also have a recall to replace a faulty airbag wire harness from supplier ZF (many manufacturers affected). If you know the VIN of the unit you want to buy, you can check pending recalls/campaigns here
https://www.toyota.com/recall . Some “S” with navigation integrated to the radio head unit also suffer from freezing units, with no particular extended warranty to cover it. All in all, I'm very satisfied with mine (LE Eco 2014). Good luck.