Asylee and green card?

Little over a year ago i received my asylum. I was married when i was granted asylum but i filed my asylum papers few year before i got married so she was not included in my asylum claim. A year ago i filed derivative asylum for my wife(she is on H-1B visa) which was approved few days ago.
Now she got a job offer and the organization can sponsor her for a green card.
Can she apply for a green card while she is an asylee?
Can she go back to her native country?

I will be grateful if someone could answer my question.

Answer:
but if she is a refugee, how can she go back just as easily? She was supposedly flying death. If she goes there and then will come back alive, it means that she lied to the Immigration. I think her status will be then canceled and she will be sent back.
Can she apply for a green card while she is an asylee?
yes
Can she go back to her native country?
yes after she granted a green card but not asylee
as an asylee you can only applied for a green after one year you are granted you asylum...

The immigration information post by website user , MyTend.com not guarantee correctness

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