can a person collect disability and unemployment

The Unemployment people ask you if you are ready willing and able to work.   So if you say no, then you won't receive  it.  The SS people ask you if you can work and if you say yes, the you won't get it.  There are some situations where the Unemployment would only reduce your SSD back pay.  And some situations where a SSA judge might deny your claim since you were getting Unemployment. The very short answer to your question is "no." But it is a complex issue that gets discussed by SSA and SS Disability Lawyers all the time.