This is the 10162nd most frequent Turkish word.
başlarına
"To their heads" or "on them" (depending on context).
In this sentence, 'başlarına' refers to the outskirts or edge areas related to the village, emphasizing the vicinity near the village.
Fırtına köyün başlarına kadar geldi.
The storm reached the outskirts of the village.
In this context, 'başlarına' implies that the problems occurred or befell them personally, utilizing the word in a metaphoric sense.
Sorunlar onların başlarına geldi.
The problems befell onto them.
Here, 'başlarına' is used literally, indicating a physical location around parts of their body, i.e., near their heads.