There have been rumors about Apple planning flexible displays for iPhones and iPad and even Macs. Apple has recently filed for or is being granted patents for which involves this technology.
The latest patent with the patent number 10,488,888 for “electronic devices with flexible displays having fastened bent edges”. Apple says in the patent that:
flexible display technologies are available that allow displays to be flexed […]
Apple files a lot of patents in the US Patent & Trademark Office. Out of them very few are materialized. But since Samsung and other competitors have jumped into and have released devices with flexible displays it is imminent that Apple comes out with a tech involving flexible displays for iPhones and iPads.