No.........but it can become blocked to certain areas by narrowing of arteries.Diabetics sometimes suffer with circulation problems,I know one diabetic man who had both legs amputated above the knee because of this.
As your heart is an involuntary muscle (that is one over which you can exert no control)then no it is not possible for your blood to stop pumping around your body;or as bednobs so rightly says,you would be dead!
However,daffy is also right that there can be temporary blockages.
But I think your "friend" is taking you for a ride if they mean a permanent stoppage.
I read in a health magazine a few days ago that when you sneeze your heart stops for a fraction of a second, so presumably if the heart stops, so would the blood flow.
You have got to be kidding jan5528, are you seriously expecting people to believe that this question is NOT a joke because if it isn't then the only place the bloody has stopped circulating in YOUR body must be around your brain.
But frostbite wouldn't stop the blood pumping round the body, that much frostbite would incur death. The tips of fingers, toes, nose etc are the areas usually affected by frostbite.
SIROAM-ETAHI............Your username is a very thinly veiled racist remark and you should be removed from this site asap. If you read jan5528's messages properly you would realise she is referring to someone claiming this to her,not saying she suffers from it!
Daffy, I agree that the user name you referred to is an absolute disgrace, it is racist, and easily spotted and translated. It should definitely be banned forthwith.