This is not something that ProSeries does, but rather an add on program of Quick Employer Forms. According to https://proconnect.intuit.com/proseries/faqs-quick-employer-forms/ you should be able to access 2019 forms. 

Will I be able to access prior-year client data after the online application has expired?
Yes, as long as you have purchased a current-year Intuit Quick Employer Forms Accountant license in order to access the online application, and your current-year and prior-year purchases exist in the same account, you will be able to see prior-year client data. For example, between November 2019 and October 2020, you will need a 2019 license in order to access your 2018 data.

If you only have a few 1099s to prepare there are cheaper online prep programs that just charge a per 1099 fee. Such as https://proconnect.intuit.com/community/lacerte-tax-discussions/discussion/re-prepare-1099-within-la... mentioned by @qbteachmt