Running away was common in many different types of pookies.
Who does it and why?
Lots of different pookies ran away for different reasons.
Divas would usually run away because their mumu/duh duh wasn't rare, or if they just wanted to cause drama. Most of the time they made sure everybody in the family knows, by shouting that they are running away.
Sad pookies ran away very often. They often ran away because they were lonely, or weren't getting attention.
When a pookie gets adopted by a meanie mumu or a pookie hater, they may try to run away. Sometimes they won't be successful, and the hater/mumu will skill them. Usually, they are able to hide in time, in a different server or an obscure part of Club Penguin island, where the hater/mumu won't find him/her.
How do they do it?
Running away can be very quiet. If it's quiet, the pookie will quickly say "runs away", or "leaves", and then leave. Sometimes they won't say anything, and will just leave.
Running away was not always secretive, however. If a pookie wants the fam fam to know that they're leaving, they may make a huge deal out of it. This is most common with divas. They will start by screaming and crying, then they will usually lock themselves in their room. They will say things like "packs up!" or "puts wittle dolly in backpack!". Then they might even sneak into the kitchen to get food for the trip. Members of the fam fam will often try to stop the pookie from running away, but the pookie will usually ignore this. If the pookie is a diva, they might say "Is weaving becwause woo are mot rare!" Right before they leave, they might say something like "storms out of iggy!" or "slams door so hard windows break!".
What Happens After?
Pookies usually go to the Pet Shop after running away. However, pookies may go somewhere else instead of the Pet Shop, such as leaving the game entirely or go on a different server. Usually the mumu or duh duh will try to find the pookie and bring him or her back, or they ignore it.