People aren't exchanging money with the vendors, just walking up and taking food. 

A few children jump into one of the larger fountains and chase each other around, giggling.

...this 'just walking up and taking food', does it involve, say, talking? As a requirement? If it does, is there a pattern to what they say that she can memorize?

Usually things are said, but not always! After the food is exchanged, something that probably means 'thank you' is said!

Okay.

That still involves approaching people, and the mere idea is terrifying, but if it's that or starve she might be able to manage it. Maybe. If she has to. Oh look she's panicking again; she grips the edge of the bench and closes her eyes and waits for the worst of it to pass.

The children flop on the ground to dry off. One of them goes and gets them both some sort of sticky rice balls.

She flinches when she hears the kid pass close to her on his way back.

She's having a hard time calming back down with this many people around. She's probably going to be here for a while.

Someone scolds the kid for going near her. People leave her a wider berth.

...the person scolding the kid really didn't help, now she's freaking out about what might be done to them - there are so many things that could, in a stunning variety of types of awfulness. She whimpers and slides to the ground and curls up tightly again.

The kid looks abashed and says something in her direction and then backs off when she looks to be falling apart. He looks distraught for a minute and then runs to bury himself in his father's robes. Everyone gives her more space.

She's not aware of any of it.

People continue rerouting traffic around the block she's on.

She eventually comes out of it enough to make her way back to her hiding place, dazedly.

She doesn't seem inclined to come back out again. Or move, it quickly becomes obvious - if they bring her finger food and put it close enough, they'll find it picked at when they return, and if they don't, well... not that.

They'll do that.

After a few days, she starts watching them when they come with the food, instead of lying there completely passively. It's kind of creepy.

Usually someone, looking a bit sad and with immaculately braided hair, will walk up to within reach of her, set down the tray of food, take away the old tray of food if there's anything left, and leave again. If she eats something they try to make sure the next time there's more of that.

Sad is worrying. She doesn't know what's going on here, doesn't even have a good guess, but they're acting like staff, and upsetting staff gets you hurt. But the alternative is to go back out... and who knows what happened to that poor boy... so. She'll stay here. And whatever happens will happen to her.

...after she thinks about that the boy brings her food, the next time. 

Well, that narrows the possibilities down some, anyway.

He mutters something aloud that she doesn't understand, before he leaves.

It's good that he's okay, for whatever meaning of okay. Just, next time someone might not be. She stays put.

Food continues to be brought. ...what happens if they sing very quietly while they bring it?

She's tenser, but it's because there's something new at all, not because the new thing is singing in particular.

Then they'll tentatively keep it up. Everyone needs music. 

(How long? they ask. 'Might be Years', he says. They have forever. Years would be all right.)

She doesn't object. She doesn't do much of anything, especially when they might see. She sleeps a lot, though she's almost always awake when it's time for them to drop off the food. Her appetite gets a little better, slowly.

 After six weeks she tentatively decides that they might not be planning to punish her, and a few days later the person who brings her dinner finds her sitting up, reading a book. She freezes, tense with alarm, when they come in, but doesn't curl up or even look away.

They put the food down and walk away, singing quietly.

The next time they bring her a book. It's handwritten and looks fairly fragile.