That is the father of Aaron... Clair's ex boyfriend that broke up with her while she was pregnant, after convincing her the two of them would be able to raise the baby...

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Please don't give up, Des. Because all we really need to survive is one person who truly loves us. And you have her. I will wait for
you. Always. I love you, Pen

DESMOND: I love you, Penny. I've always loved you. I'm so sorry. I love you!
PENNY: I love you too.
DESMOND: I don't know where I am, but--
PENNY: I'll find you, Des--
DESMOND: --I promise--
PENNY: --no matter what--
DESMOND: --I'll come back to you--
PENNY: --I won't give up--
BOTH: I promise. I love you.