Cross Necklace

After any hit there is a window where nothing can touch you, and this stretches it. Against a boss that hits once and swings away, that is worth very little. Against something that fills the screen with bodies or projectiles, it is the gap between taking one hit and taking four. The Destroyer and Skeletron Prime are the standard cases, since both surround you with contact damage and the extra frames turn a death spiral into a survivable pass.

Star Veil is built out of this, and the two invincibility effects do not add together, so wearing both accomplishes nothing. It does combine with the dodge accessories: Master Ninja Gear, Black Belt and the Brain of Confusion all get a longer post dodge window when this is equipped. That interaction is real and frequently missed.

It does nothing at all in PvP. In the other direction, wiring a slime statue and a heart statue into a sealed room gives you a steady supply of harmless hits, and with this equipped that keeps you effectively untouchable the entire time. It is the standard build for anything that requires sitting still without dying.