severance and unemployment please help

I recently was terminated from my job, they offered me severance pay over the phone. They said I would receive it every two weeks for two months they would give the checks to my sister who is employeed their still with the company.I applied for unemployment, I have never did this before so I asked my former employee the reason for my termination. They said employee at will,I let unemployment now, They mailed me a check I was not sure about the severance and if they were really going to give it to me. Today They told my sister to tell me to call Human resources, so I did . They asked me if it was okay to give my sister the check I told them that when you terminated me thats what you already said you would do. She said I need to ask as a percaution. I than asked her why I was terminated to see if she would give me the explaination she just said employee at will. No reason, I tried to call unemployment to ask them what I should do, I left a brief message on the answering machine. No one has called me back yet today, Could some one please expain what I need to do. What did she mean by percautions? Is it normal to get severance? And on the check their still taking out for Medical and Dental also Credit Union, It does not say severance should it? I do not want to cash it Or the unemployeement I'm afraid I need advice I do not want to get in trouble for not knowing what to do. Thank you