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They only found out two weeks later; after the alleged private funeral and after Tony failed to find their Phil Coulson in any kind of listing in America. It didn't take long for Natasha to find him in SHIELD's database though. He was in a private hospital in Florida, registered under the alias David Abram, and in critical condition.
Tony flew them down in his private airplane on the same day. Fury didn't bother to stop them. It was strange and unsettling to see the formerly sturdy man look so frail in his hospital gown, surrounded by various machinery that was keeping him alive. The Avengers set up a rotation immediately - at least one of them would be present at all times. Phil Coulson believed in heroes. It was time they returned the favor.
It took two weeks before the agent was moved out of Intensive Care. Clint had set up a nest in the corner of Coulson's private room (if only because there was no space in the ceiling, he checked), watching, unwilling to miss a single twitch. He was only ever gone when Fury sent him on missions. Natasha visited every day - partly out of the same concern as everyone else but mostly to make sure Clint stayed fed. Most of the time, she scared the few nurses who managed to notice her presence. Clint thought she got a kick out of that.
Steve took the daily night shift and kept watch vigilantly. Bruce quietly kept him company. Tony's presence was the most sporadic. He didn't like hospitals. But it was during his night watch that it happened. Steve had stepped out to get them coffee. Tony was half dozing in the chair next to Coulson. When he jerked awake again, there was a magazine over Coulson's face. He blinked once, twice.
"Agent?"
No response.
He moved the magazine away. Coulson looked as asleep as ever. Tony prodded his side. No reaction.
"You know, I don't believe in ghosts," Tony declared to the room and sat back down, throwing the magazine back on the side table.
It happened again two nights later. Steve was there this time. Neither of them saw it happen.
"What's going on? Is he awake?" Steve looked both concerned and hopeful.
"No? I don't know." Tony was poking at Coulson again, looking for a reaction. Nothing.
"I'll get the doctor."
The doctor couldn't explain it either.
The third time it happened, it was a week later and Clint was the one in the room with Tony. Again, neither of them saw anything.
"The hell?" Clint shook Coulson lightly but got no response.
"Okay, this room is officially haunted."
And so it went. By the seventh time, everyone noticed the pattern.
"You're the key," Natasha looked at Tony pointedly. "Somehow."
"I'm really not that into Agent Coulson."
"It only happens when you're sitting next to him at night," Bruce added.
"Meaning?" Tony squinted at him. Bruce held out his hands in a light shrug.
"We'll all keep watch tonight," Steve suggested. No one argued.
And so it went. Tony grudgingly sat next to the comatose agent and did absolutely nothing while everyone else kept watch. Clint was the one who noticed it first.
"Guys."
Everyone looked. Coulson's hand was moving. It found the magazine on the table, pulled it over his face, and fell back limply on the bed. Silence reigned for a few seconds. Then all eyes were on Tony.
"It's your arc reactor."
"Seriously? It's not even that bright."
Still, Tony showed up every night after that.
Two weeks later, Agent Phil Coulson regained consciousness. All of the Avengers, sans Thor, were there to greet him.