Elliot hadn't meant to overdose. He had been given some sleeping pills by George because his sleep rhythm had been disrupted by the odd hours SVU detectives worked. George had told him, he thought, to take 2 pills. So Elliot complied and took some and went to bed with George. They were watching some TV together, when Elliot suddenly blacked out.
George panicked and checked Elliot's pulse. It was still there, but what had happened? He frowned, thinking, and then remembered. The damn pills.
He called an ambulance and then did what he remembered from his ER rotation. Elliot was admitted overnight; fortunately it wasn't a severe overdose.
When Elliot woke up, George hugged him tightly and whispered "Don't do that again. I promised I'm not going anywhere, you need to promise too." Elliot held the smaller man closer and whispered "I'm not going anywhere, George." They hugged for a while after that.