Why does the Widow Douglas come to the Welshman’s home to take care of Huck?

The Widow Douglass takes care of Huck because all of the physicians are busy at the cave. She's also a caring, compassionate woman.

The physicians were all at the cave, so the Widow Douglas came and took charge of the patient. She said she would do her best by him, because, whether he was good, bad, or indifferent, he was the Lord’s, and nothing that was the Lord’s was a thing to be neglected.