I worked for a company as a salaried employee with taxes taken out of each paycheck. After being employed for several months as a salaried employee, my employer switched to a 1099 company. If I no longer work for this company, am I eligible to file for unemployment benefits from this employer?

After the switch, did you become a so-called "independent contractor" for this company?

You can claim unemployment benefits for the period during which you were employed, assuming you are not now fully employed, and are seeking work. If your received 1099 income, of course, you would have to report that in your application.