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Cordelia had clung to Angel's arm shortly after their first real conversation, after he had found her hiding in the dumpster thanks to his weirdo skulking behavior and had saved her from the creepy arm she found.
That's how their hugging relationship started, with Cordelia holding on to Angel and him tolerating it. At the time, he must have wanted to embrace Buffy a lot more than he wanted to hold her, but he was kind enough to never shrug off her effusive affection.
Doyle's death, when he jumped into the light and sacrificed himself to save Angel, was the first time Angel actually hugged her mutually.
When she inherited Doyle's visions, Angel rushed over to catch her before she could fall. Those weren't technically hugs, but they felt like embraces all the same, especially when the years passed and Angel let go more and more slowly.
They had a lot of hugs since then. Relieved hugs, like when Angel rescued Cordelia from that auction and she flung herself at him while he was in full vamp face, crying out that she knew he would find her. Joyful hugs, like when Angel bought her new clothes to make up for being a stupid ass, and Cordy was so happy to have her friend back that she hugged him, kissed his cheek, and even did a happy dance (which Angel joined in). Worried and sad hugs, like when Angel cautiously held her as she wept into his chest after seeing that guy stab himself in the eye. Reunion hugs, like when Cordelia squealed and embraced Angel after he came back from Sri Lanka, long and slow, glad that he was back home where he belonged. (The tone of the hugs had changed around then. Cordelia wished she had noticed.) Slightly awkward, but very affectionate hugs, like the time she had returned to consciousness on her birthday, Angel had made an aborted movement before he held her and said "I thought I'd lost you," and Cordy had closed her eyes. (Later, she wondered if Angel had been thinking about kissing her.) Supportive hugs, like the time they reversed roles and Cordy held Angel when she came from her vacation and discovered that he had lost his son.
There hadn't been a lot of hugs in the past year. Her memory had been gone, and she didn't remember her own name, much less how wonderful it felt to hug Angel. And then Jasmine took over her body, and she only allowed Cordelia to hurt Angel. At least she hadn't managed to taint their hugs.
So many years together, and so many hugs for her to treasure. Angel's arms have comforted her, made her feel safe, and made her heart beat a little faster countless times. Still, it's not enough. If Cordy had her way, she would be there with Angel until he shanshued, just like she naively promised years ago. Hell, she would stay with Angel until the end of his unnatural life if she could. And she would never stop hugging him or kissing him. But unfortunately, that can't happen.
Now, she's back, but only for a short time. After she makes that joke about how the hospital smells like ammonia soaked death, Angel moves in for what he doesn't know will be their final embrace.
This time, he's the one who clings to her with all of his powerful strength. It's a fitting conclusion, considering how Angel and she started this hugging thing. If she were real and not just an astral projection, Cordelia might be complaining about the way his hands would leave bruises on her shoulders. As it is, she hugs him back tightly, closing her eyes and savoring one last hug.