author's note: Insert the usual witty disclaimer here about how I don't own this universe or any of these copyrighted characters.
I suspect that Filch the caretaker has not come to Hogwarts yet, but I left him out of this story anyway to be on the safe side.
Hagrid was sobbing, with his face buried in his enormous hands. Students passing by on their way to and from their rooms kept their distance. Dumbledore approached him quietly, making no noise on the carpeted common room floor. "Hagrid?" he said.
Hagrid looked up. His face was shiny with tears. "I didn' do it, Professor. I never ... but the headmaster's expelled me ..."
"Hagrid," said Dumbledore gently, "I believe you." Hagrid's face brightened a little.
"But," Dumbledore continued, "I'm sorry, that doesn't mean you will get to stay here as a student." Hagrid bowed his head, screwing his eyes tightly shut.
"However, there is some good news. I have a plan, and if it works, you are not going to have to leave Hogwarts."
Hagrid looked up. "Eh? How?"
"I think I am right in venturing to suggest," said Dumbledore, "that what you really want is a place where you are needed. A place where you can be useful, yes?"
"O' course!" exclaimed Hagrid eagerly. "But ... I'm not much of a wizard, am I. An' now they snapped me wand, I can't do anythin'."
"You are still a wizard, wand or no," said Dumbledore firmly. "But there is even more good news. How would you like to live at Hogwarts and never have to go to class or do any homework?"
Hagrid looked as though he could not believe what he was hearing. The joy on his face was impossible to describe. "I'd give anythin'! That'd be ... wonderful, like a dream come true fer me! But how? What're yeh talkin' about, Professor?"
"I am suggesting that you might stay here as gamekeeper," said Dumbledore, smiling. "If we can persuade Headmaster Dippet, that is. You'd help maintain the grounds, grow the school's vegetables, feed the giant squid, that sort of thing. You like the outdoors anyway, and you're big and strong. I think it would be right up your alley."
Hagrid jumped up and hugged Dumbledore tightly, lifting him right off his feet. Dumbledore gasped, "Easy, Hagrid!" and Hagrid set him down, looking embarassed. Dumbledore straightened his robes, a little breathless. "Try not to underestimate your own strength," he said kindly. "Just pack your things up neatly in your trunk, tidy your bunk, and make yourself as presentable as possible. Then you can bring your trunk to my office and wait there while I talk to Professor Dippet."
Hagrid charged up the staircase and disappeared, almost knocking aside a couple of Gryffindors who were on their way down to the common room. Dumbledore chuckled affectionately as he watched the third-year boy go. A snatch of enthusiastic (if off-key) singing, in a deep bass register, floated down the stairs. Muffled bangs and thumps punctuated the song as Hagrid packed his trunk. Dumbledore turned and left the common room, and went to Dippet's office.