Hi there. Yes it is possible to have a positive result on an hpt after miscarriage. This happened to me.....but I wasn't too far along. Maybe 4 weeks. I also had pregnancy symptoms for about 8 days and then they dropped off. I'm not sure how long it will take. That may depend on how far along you were when yo had the m/c. I'm really sorry for your loss.
try posting on the pregancy forum , they are pretty accurate with info on there about hormones and blood results !
The pregnancy hormone HCG will most likely still be in your system after 1 week of a miscarriage. I'm not sure how long it takes for it to go down to 0 again. I have heard of some women going back to 0 around 6 weeks, and others take a little bit longer. I think that might depend on how far along you were. So answer to your question...Yes HCG will still be in your system after 1 week after a miscarrige.