The cores can handle more than one thread at once. This is the beauty of concurrency. The OS has a component named scheduler which takes care of providing access to the threads that want to be executed. Basically, it takes care of switching the threads to access the core and execute the logic.

If you provide the more threads its going to occupy memory. Each thread can take up to ~1MB of memory. If you have threads occupying memory more than your VM then you will run into Out of Memory Exception and the application will crash.