if you are terminated for poor work performance or have a reduction in pay in excess of 20% you may qualify for unemployment benefits.
however you may have screwed yourself by refusing to sign that write up, many employers require that write ups be signed and refusal to sign is grounds for termination that would most likely disqualify you from getting unemployment as refusal to sign it is intentionally violating policy.
signing it is not a confession of anything it simply acknowledges that you were aware that you were written up.

