OK this is a strange one:
Is there a way someone can develop native C applications or libraries for Android without using the Android NDK?
What was happening before the NDK was released? (It’s not there for too long, I think it was released only one or two years ago).
Before the NDK was released, the only officially supported way of developing Android applications was to use the Android SDK and writing your applications in Java.
As others have mentioned, it’s possible to cross-compile some applications as completely stand-alone and run them on a rooted phone. The downsides of this should be obvious: very few people will be able to run your application (they also need to be root, plus you won’t be able to get your application up on the Play store); and you might even run into compatibility problems yourself across different devices e.g. if you rely on dynamic linking against various libraries (which you might need to do in order to keep the size of the binary down).
TL;DR: it’s possible, but severly limited, and not recommended.