Not typically.
Employees receive a W-2 form which shows the amount of wages paid to that employee as well as federal income tax withheld.
1099 forms are issued to independent contractors. A homeowner who hires a painter to paint their house for a $1,000 has to issue a 1099-MISC form to that contractor for miscellaneous income of $600 or more. If the painter charged less than $600, the homeowner would not have to report it to the IRS.
W-2 forms typically show that an employer has withheld federal tax, social security, medicare and so forth while a 1099 form typically does not show federal income tax withheld (it might, but typically it doesn’t). An employee is not likely to receive a W-2 form from an employer as well as a 1099 form. I can’t think of any cases where a situation like this would arise.