So basically, if you possess a drowned and throw a trident that has Loyalty, more often than not, you keep the original trident in your inventory, but the trident you threw comes back to you and you pick it up. You can keep doing this until your inventory is full, at which point the tridents start surrounding you, which is pretty hilarious.

Also, if you have Emancipation and stop possessing the drowned, or if the drowned dies, the tridents continue to follow you, even as a spirit, but you can't pick them up.