Special arrow quivers?

[Former-GM-Circe]

You don't automatically lose anything a pet is holding when you log off.
The game tries to fit it all into your character's inventory, and what it can't fit in, it then drops on the ground.

As for the 15 limit, it is 15 "slots", whether the slots are 15 lots of 1 mucus, or 10 lots of 1000 mucus and 5 lots of 1 mucus.
The limit on a single slot is however many you can drop for it to pick up. So, pretty much your wait limit, unless a player with a larger limit drops a full limits worth. In that case, you won't be able to pick it up, either, so it is generally useless.

From memory, custom looting pets hold more than 15.