This question has its genesis in a common situation: a PC sends his familiar reconnoitering.
The familiar travels beyond the range of both direct observation (vision, hearing, etc.) and find familiar's telepathic communication (see PHB p. 240). When the familiar does not return at the appointed time, the PC comes to suspect something's wrong. And in point of fact, the familiar has been killed off-camera. The player asks how his PC, who has no other relevant spells and no magic items, might determine whether the familiar is alive or dead.
Debate ensues, leading to a deeper question about the nature of find familiar. Once past the limits of telepathy or direct observation, does a familiar turn into a black box? In other words:
What, if anything, can the caster of find familiar ascertain about the state of his familiar purely by dint of the spell itself?
- Does the caster automatically know whether the familiar is alive or dead?
- Does the caster automatically know whether the familiar is in its pocket dimension?
- If the caster uses an action to dismiss the familiar into its pocket dimension, does the caster know that the dismissal succeeded?
- If the caster attempts to use an action to dismiss the familiar into its pocket dimension, but the familiar has been killed and has "disappear[ed]," what does the caster learn? That the familiar is dead? That the familiar has disappeared, but not specifically that it's dead? That the dismissal failed? Nothing?
- What if the familiar is already in its pocket dimension? Does the caster learn that the familiar is in its pocket dimension? That the dismissal failed? Nothing?