Company sold, not sure of my status

Last week the company I work for was sold. On Friday all employees were paid for all hours worked up until that day (even though normally we receive pay every two weeks). The new company management told me to report to work today (Monday) but required me to fill out a new employment application.
There is a very good chance that they will offer me the same position with fewer hours and for lower wages. I do not want to take that offer. If I do not, will I be eligible to collect unemployment compensation based on the former company's contributions to the fund, or does my refusal to take the same job at a lower wage and for fewer hours from this new company qualify me as a "quit" rather than a layoff? I live in FL.

Thank you.