Bonding is not required I have logged out leaving a fresh tamed mare in Yamotsu mine after going after a fire beetle. I'd left it for dead, but when I logged in next day it was there beside me.
Many of the pets that are lost are lost at server maintenance time. To give an example:
At the point that the server makes it's last save you are down in the dungeon, beside your pet, vetting and all unaware - You return home and log when you see the notice, or you lose connection when the server goes off line.
Following maintenance the server is re-started at the point of the last save, all *available* mobiles are restored to where they were at that point. You were in the dungeon with your pet. Therefore the pet is restored there. You didn't log till after that point, so autostable hasn't happened yet (pardon the time paradox) However although you were there at that save point the first time around, you're not there now. You've gone to bed. So the pet is in game, all alone. If you're lucky, and know what's happened, you can return to the dungeon and find your pet close by, sometimes needing re-taming.