A client that has an S-Corp but received payments issued to her personal SSN instead of the corporation EIN, can I issue the corporation a 1099 form from her personal SSN to offset that income from her personal on to her corporation?

I've had this happen... I entered 1099 amount on Schedule C income then did offsetting expense on Other Expense line  as "income reported under S Corp EIN xx-xxxxxxx"    

where did the money get deposited?

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).

Happy day...I did not want to pass up the opportunity to throw gas on the fire.  Depending on the type of business the person is in, it may be perfectly reasonable for them to receive a 1099-NEC, despite having an S-corp.  See Fleischer v. Commissioner.

<insert fire references from popular '70's songs here>