Do familiars get death saving throws?

Question

Do familiars summoned by the Find Familiar spell get to utilize Death Saving Throws, or do they die immediately when they reach 0 hit points?

Answer 1

No, they just disappear.

Find familiar states (PHB, pg. 240):

When the familiar drops to 0 hit points, it disappears, leaving behind no physical form. It reappears after you cast this spell again.

It does not die, nor does it fall unconscious. It just disappears.