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There are quite a few kinds of 1099's.  Do you mean a 1099 that you will get for working as an independent contractor?  Or something else--like a 1099R, 1099DIV, 1099INT. etc.?

If you worked as an independent contractor--which I am assuming is why you are mentioning a 1099---then you pay self-employment tax for Social Security and Medicare and depending on how much you made, ordinary income tax.  None of that is withheld from your paychecks when you are an independent contractor, so you pay it all yourself.  If you are receiving unemployment compensation while working as an independent contractor it is your responsibility to learn and understand your state's rules about that.    When you certify for unemployment benefits you must be asked if you worked or earned income.....

https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922

https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax

https://ttlc.intuit.com/questions/2903027-how-do-i-report-income-from-self-employment

https://ttlc.intuit.com/questions/1901340-where-do-i-enter-schedule-c

https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct

And you did not ask but might find this helpful:

Unemployment compensation is taxable on your federal return.  Enter your 1099G for unemployment in Federal>Wages and Income>Unemployment

You might need to get your 1099G from the state’s unemployment site.

STATES THAT TAX UNEMPLOYMENT BENEFITS

AZ, AR, CO, CT, DE, DC, GA, HI, ID, IL, IN, IA, KS, KY, LA, MA, ME, MD, MI, MN, MS, MO, NB, NM, NY,NC, ND, OH, OK, OR, RI, SC, UT, VT, WV, WI

Unemployment compensation is taxable on your federal return.  Enter your 1099G for unemployment in Federal>Wages and Income>Unemployment.  You might need to get your 1099G from the state’s unemployment site.

STATES THAT DO NOT  TAX UNEMPLOYMENT BENEFITS on the state return

AK, CA, FL, MT, NH, NJ, NV ,PA, SD, TN, TX, VA, W