Here is a posting I came across. The bird is a budgie... just imagine how much fun it must be... in the wild, to eat, bath, and chase other birds around...
Does this lady need to try to catch/rescue this bird as I initially suggested? Or my another thought was... that the bird is probably having huge fun while it's summertime, instead of being locked up alone in the cage (not always a case of course, but could be)
What you think?

would someone tell me please - can budgies "walk" along cage walls like cockatiels do using their beaks? can they jump from a lower level to a higher placed perch? (I have never had a budgie)
I will be bringing her a cage... trying to organize things in it

To your questions the answer is yes to all....
My 2 budgies are just like my tiel....

The bird is in danger as long as it's free, and escaped budgies usually don't last too long in the wild. We don't know whether it's having fun or not. Sure it's free, but we can't tell whether it's getting enough to eat or how threatened it feels by everything it has to contend with. Like the risk of predators, and competing with other birds for food.

thank you.
Of course the question about "having fun" was stupid, I know
Last night we had huge, enormous thunderstorm. Certainly no fun could have been had this way. I was even worried if the bird made it thru (the temperature stayed warm, though, 69F) but the lady said she had seen the bird today after the storm
I delivered her a cage with some bird seed, some millets, and even couple of toys. We will see if the bird decides to go in. Not sure what else I can do

But if what the lady says is true, I am just amazed that this bird survived for so long in the wild...

can budgies walk on a half-inch grate?

Yes mine can

Regardless of whether or not the bird is living free and not in a cage you have to consider a few things. Avoiding predators, finding food, finding water and no care. If the bird falls ill it dies. In captivity the bird would always have access to food and water, a lack of predation and veterinary treatment when necessary. Another issue is released species can wreak havoc on the natural ecosystem

So far feral parrots haven't been an ecological threat, since it seems like they can only survive in areas that are heavily populated by humans. They get most of their food from non-native plants and bird feeders. But escaped budgies usually have a very short life expectancy, and this bird will be much better off if you can catch it.

Some update,
Now there are two loose budgies in different parts of the city (I am letting both households borrow my cages). There is no much update on the one I posted about (a blue one).
But another popped up not far from where I live (somebody sees him coming to eat to her feeders). Interesting, she said at first she saw two bright yellow birds but it was the only time she saw them together. I also contacted birds people from my city and one guy came over there with me tonight, he is a big bird specialist and he has caught escaped birds before.
First of all, we didn't get to see the bird, even though the lady of the house saw the bird just 30 minutes before we arrived. The guy looked at the picture she took and said it was English (yellow) budgie. He thinks that the second bird might have gone... back home.
He also said that this specie is native to deserts of Australia, and they are designed to stay in extreme climate and can have water as rare as once in 14 days (DID YOU GUYS KNOW THIS?)
he also gave the lady some advice on how to handle this bird. Offer just a finger, not a whole palm. Then if the bird steps on the finger, grab him by his foot (the bird will scream and try to release) then using another hands grab the whole body.
he also said that she can soak it completely wet out of a garden hose very quickly and then they won't be able to fly so she can grab the bird (he said budgies do drown in water, they can't get out)
Since the lady has some feeders full of food (the food looked good to me), its unlikely that the birds will find my cage attractive to get in... There is millet inside it, but still...
I have got an idea to print some posters and hang along the street that has backyards adjacent to hers. What if the second bird really just "went back home"?