An object whose fate is in some way unanswerable with our current knowledge is said to have an unknown fate. The simplest way that the fate of an object can be unknown involves the question of whether or not it exhibits infinite growth. For example, the fate of the Fermat prime calculator is currently unknown, but its behaviour is otherwise predictable.
A different type of unknown fate is that of the Collatz 5N+1 simulator, which may become stable, or an oscillator, or have an indefinitely growing bounding box. Its behavior is otherwise predictable, and unlike the Fermat prime calculator the population is known to be bounded.