It is perfectly possible to write a function in pure Java that would never terminate when called with parameter values outside of the domain for which it is defined. It is also possible for it to yield an incorrect value.
Your statement that such a function would throw an exception is false.
Ensuring a function is only called for the domain it is defined on is entirely at the programmer's discretion regardless of language. Some choose to ensure all functions are defined for all possible values, but that's obviously impractical due to combinatorial explosions. Types that encapsulate invariants are typically seen as the solution for this.
I didn't claim that all functions are either correct or throw an exception in Java. I said that UB doesn't exist in Java, in the sense of a Java program that compiles, but for which no semantics are assigned and the programmer is not allowed to write it. All situations that are UB in C or C++ are either well-defined in Java (signed integer overflow, non-terminating loops that don't do IO/touch volatile variables), many others throw exceptions (out of bounds access, divide by 0), and a few are simply not possible (use after free). Another few are what the C++ standard would call "unspecified behavior", such as unsynchronized concurrent access.
And yes, it's the programmer's job to make sure functions are called in their domain of apllication. But it doesn't help at all when the compiler prunes your code-as-written to remove flows that would have reached an error situation, making debugging much harder when you accidentally do call them with illegal values.
Your statement that such a function would throw an exception is false.
Ensuring a function is only called for the domain it is defined on is entirely at the programmer's discretion regardless of language. Some choose to ensure all functions are defined for all possible values, but that's obviously impractical due to combinatorial explosions. Types that encapsulate invariants are typically seen as the solution for this.