Hi there, @lilisoleil.
I'd be glad to help you turn off the email notifications sent to your employee from your QuickBooks company.
You'll have to delete the email address of your employee in their profile and replace it with a dummy account. Here's how:
- Go to the Payroll menu, select Employees.
- Select the name of the terminated employee.
- In the Profile section, click the Pencil icon.
- In the Email field, manually erase the existing email and replace it with a dummy ones.
- Select Done.
I've added a screenshot to see how it looks like:

I've included this article to know more about managing your employee in QuickBooks: Invite your employees to QuickBooks Workforce to see pay stubs, W-2s and more. This contains frequently asked questions at the bottom part of the article.
I'll be here if you have other questions, don't hesitate to comment below. Take care and have a wonderful day.