It's generally true that a pet parrot that flies away has a very low chance of survival. Many of these domesticated parrots are not native to the region where they are kept, and the natural environment poses significant threats, such as predators, which drastically reduces their chances of making it. 
Parrots are not indigenous to many areas where they are kept as pets. Outside of their human homes, they face dangers from stray cats, birds of prey, and other predators. This makes it very difficult for them to survive. Furthermore, a lost pet parrot typically doesn't find its way back home unless it has been specifically trained to do so, making the chances of its return quite slim. These factors are major reasons why lost parrots don't survive.
Will a Parrot Feel Sad When Separated from Its Owner?
If a parrot has formed a strong bond with its owner, it will often feel sadness and distress when separated. Parrots are very emotional animals, and leaving their owner can cause considerable anxiety and feelings of insecurity. They may also experience difficulty adapting to a new environment or a new owner. This emotional distress highlights the importance of keeping these pets safe from getting lost.
However, if the parrot didn't have a good relationship with its previous owner, it might not experience sadness when moved to a new home. That being said, a new owner needs to be patient and provide plenty of attention and care. With time, the parrot will likely adjust to its new environment and bond with its new owner, eventually becoming tame and affectionate.
When parrots are sad, they may start plucking their feathers out one by one, experience a noticeable decrease in appetite, and gradually lose weight. If you notice your parrot exhibiting feather plucking behavior, it's important to seek veterinary care. A stable and comfortable environment is key to promoting the health and wellbeing of the parrot. Ensuring they thrive is a part of responsible pet ownership, especially when dealing with these highly sensitive birds, so keeping them safe to prevent loss is paramount for their survival.