Why does the minister's wife send Miss Emily's relations a letter in "A Rose for Emily"?

The ladies want to write to Emily’s relatives to intervene for her in the matter of Homer Barron.
Emily had a man, Homer Barron, who was not the marrying kind—so he said. The townspeople were not sure who was going to win. Emily was strange enough that she might have won him over, but Homer was stubborn enough that he might have held out.
The case of Emily and Homer was complex. The townspeople were concerned that Emily was going to kill herself when she bought arsenic. The women of the town felt that eccentric Emily was a bad influence on other young ladies because of her relationship with Homer.
No one knew how to proceed. The men wanted to leave her alone. The ladies convinced the Baptist minister, who was not of Emily’s religion, to talk to her.

He would never divulge what happened during that interview, but he refused to go back again. The next Sunday they again drove about the streets, and the following day the minister's wife wrote to Miss Emily's relations in Alabama.

We do not know what she said to this minister, but it must have been something that caused the minister's wife to write to her family. Miss Emily was peculiar, and not quite stable. Clearly the minister thought so, and so did his wife.
As a result, Emily had “blood-kin under her roof again.” However, Emily did not become a social butterfly after that, suddenly engaging with the town. The townspeople were not sure what was happening because she did not really communicate. She seemed to be preparing for a man, and then nothing happened. Homer was never seen or heard from again.
It was not until years later that they found out that Emily had killed Homer, and that he had been in bed next to her for years as a rotting corpse. She got to keep him after all, even though he was not the marrying kind.

The man himself lay in the bed.
For a long while we just stood there, looking down at the profound and fleshless grin. The body had apparently once lain in the attitude of an embrace . . .

Emily never left the house, so no one ever realized what was in the house. When there was a strange smell, they just sprinkled some lime because it would have been rude to ask. The townspeople were afraid to confront this lady about taxes, so there was no way they were going to find out about Homer.