I'm pretty sure you have to be either US citizen or PR to claim UI...
if you can claim UI, there is no need to wait for the company-offered
package (serverance) to run out first, provided you sign the liability
waiver (most people have to sign to get the serverance. the waiver basically
says you give up the right to sue the company). the "waiting" time between
the layoff and starting to claim UI is one week.
the MA government site for UI: http;//www.mass.gov/dua
