She can't legally apply without lying.
If she answers truthfully, she'll be denied.
If she lies, they may still catch her, but this isn't the "how do I break the law forum."
There is NO WAY she's going to be magically transformed from illegal to legal no matter who she marries or how many children she gives birth to here.
There's a ten year ban for her and she'd need to get a waiver on that and that's unlikely and an immigration lawyer is where you'd have to start.

