No. The same procedures that apply to land borders also apply to the airport. You will not be allowed to fly out of Moldova if you are not accompanied by an adult who has legal responsibility for you (such as a power of attorney document).
If you arrive in Moldova without an adult, or with an adult that does not have documentation to show s/he has been granted temporary legal guardianship, the Border Police will notify the Guardianship Authority, who will come to assess your case and ensure your safety.
You may need to wait in Moldova while the Guardianship Authority assesses your situation and figure out the best way to help you. If needed, the Guardianship Authority will make sure you have a place to sleep (you will be allowed to remain with your caregiver if you are traveling with an adult, unless they suspect you are unsafe with this person).