This is the 7912th most frequent Japanese word.
垂れ
"垂れ" (tare) means "hanging," "drooping," or "sauce" depending on the context.
In this sentence, 垂れる (to sag or hang down) describes the physical state of the roof that is bending downward due to age or degradation.
古い建物は屋根が垂れてきている。
The roof of the old building is sagging.
Here, 垂れる is used to describe droplets of dew hanging or dripping down from the surface of leaves.
葉っぱに露が垂れているのが見える。
I can see dew dripping from the leaves.
In this context, 垂れる expresses the state of an object, the curtain, hanging loosely as part of its intended positioning.