Sometimes the appendage is big enough to be considered a creature on its own, or even an object with specific traits (like an hydra's neck and head).
The closest example I can think of right now is a roper strand, which is pretty close to the tentacle-thing discussed.
It could be attacked, severed, sundered, broken (treating it like a lenght of chain, maybe), but probably not grappled following the nowmal rules. The sheer size and shape of the thing won't allow it.
If the fighter wants just to block further attacks, it could be grabbed (grappled, using the usual rules) to hinder further actions and even pinned, but aside from that nothing more - so no move, damage, or tied up.
Mostly GM's call, with some on the fly modifiers to apply, and some limitations compared to a more standard situation, but still doable.