I have worked part-time 20hrs a week for 2 years for this employer. They are now asking me to be a contracted worker, doing a different job and be a 1099 employee. If I decline the offer to be a 1099 employee, can I still collect unemployment, as they no longer want me in my original position.

Won't you still be employed? Isn't unemployment for if you're unemployed?

Jtm004 is saying if the change to contract work is turned down. Unemployment requires that you apply for x number of jobs per week, and usually requires you to take something you get offered. I think the point is whether a contract job counts for that.

Your job is not being eliminated due to lack of work. And you would be technically quitting the "new" job and would not be eligible for unemployment benefits. I'd stay on this job and take the time to look for another job that will be taking taxes out of your pay and contributing toward the unemployment benefits. As you know being a 1099 employee or contractor would not allow you to file for unemployment benefits if somehow your "new" job got eliminated. This no doubt is another cost cutting measure of your company.