Let's take this a bit at a time:

"can I issue the corporation a 1099 form"

Corporations are exempt from 1099-NEC reporting, for the most part.

"from her personal SSN"

Only a Business would be subject to issuing 1099-NEC, and she is not running a business outside of the S Corp.

"to offset that income from her personal on to her corporation?"

Nope. None of that is going to make sense.

She can send a W9 to the issuer, who would Void the Individual SSN 1099-NEC. There is no reporting for the S Corp except for specific services (law firm, for instance).

She gets Payroll. 1099-NEC is not part of her relationship between herself and her employer (the S Corp).