She has already become a permanent resident. The Affidavits of Support (both from you and the joint sponsor) are fixed and cannot be cancelled. The obligations will continue indefinitely until one of the conditions listed on the Affidavit applies (e.g. she becomes a citizen, earns 40 quarters of SS credits, gives up permanent residency and leaves the US, dies, etc.). Both you and the joint sponsor accepted the risks and consequences when signing this. In practice pretty much no government will sue people for obligations under the Affidavit of Support because it's too expensive to sue in federal court.
She could pay the $165 fee herself. Even if nobody pays it, she remains a permanent resident. Not having the plastic card won't matter at least for the first year because she already has a temporary green card of 1 year.
As a permanent resident, she can leave and re-enter the US. Without applying for anything else, she can use a green card to re-enter after an absence of up to 1 year. With a Re-entry Permit, she can return during the validity of the Re-entry Permit, which is 2 years. Even if she returns with just a green card after an absence of more than 1 year, she can (and often will) still be let in. It's at the immigration officer's discretion. Alternately she could apply for an SB-1 returning resident visa to return to the US. Regardless of the length of the trip (less or more than 1 year) she needs to maintain residence in the US, or lose her permanent residence. What counts as maintaining residence in the US is subjective, and again at the immigration officer's (and immigration court's) discretion. You have no control over any of this. Just because she leaves or has left for a certain amount of time does not mean for sure that she cannot enter again as a permanent resident. The only way to be sure is if she herself voluntarily files I-407 at a US consulate to give up her green card.
If she is a conditional (2-year) permanent resident, then she can apply for Removal of Conditions by herself after divorce. She should be approved as long as the evidence shows the marriage wasn't fraudulent. You have no control over whether she gets approved or not. If she leaves the US and is outside the US after the 2 years passes and hasn't applied for Removal of Conditions, then that will also cause her permanent residency to be lost.