Chosen Solution
After cleaning both MagSafe power cord adapter and port, cord now stays green even after unplugged from Mac AND unplugged from electrical outlet. What’s wrong?
The magnet can collect very small metal debris. You might get a magnifying glass and check the plug and port for metal stuck to it. If you don’t find anything and the problem persists, don’t risk your MacBook. It’s better to get a new one or take what you have to Apple and let them check it out. What did you clean it with? 91% isopropyl alcohol should be acceptable.
With the magsafe adapter still staying green after being unplugged from the wall, I have to ask, are you using the original charger that came with the computer or a official apple magsafe charger, or are you using a unbranded or third party charger?