Unless they file a joint return, she will not be required to file a return unless she earns sufficient reportable income to require filing. She may have to file a return to get any economic rebate checks that might be required.
SSD does qualify for the rebate check, but she has to file a return to get it.
He is not able to claim her on his taxes.
The only filing status available to two people who are married is:
Filing a joint return or fling married and seperate returns.