If you resign your position or quit you are not entitled to receive unemployment benefits. If you were fired (but not for willful misconduct) then you can receive unemployment benefits.
If you receive unemployment benefits your boss's unemployment insurance rates go up. They are capped at a point (around 5%).
Many times, your boss will try to claim that you quit your job so the company avoids an insurance rate increase. This is totally unfair, but it happens.
If you suspect this to the case here are a few tips:
First, document the fact that you did not quit by writing a letter to the company stating that fact. That way they can't claim that they reasonably thought that you quit.
Second, show up for work the next day ready to work. Of course, when the company asks you to leave, then leave without incident, and this is strong confirmation that you were terminated.
Third, confirm the names and contact information of witnesses who saw you get fired.
If you or anyone you know believes that you were terminated unlawfully then contact the employment lawyers at The Bartinik Law Firm, PC, 100 Fort Hill Road, Groton, CT at 860-445-8521 or toll free at 888-717-4211.