Literally stops.
Vanezis claimed that the ‘runs’ of blood on Sheila’s lower arm were from her neck wound. He claimed that the darker spots, were in effect, where the runs came to an end, i.e. stopped flowing any further on her arm. The darker spots are supposed to be caused by the blood having collected in one place, due to the run not flowing any further.
The blood spots are darker because they came from the jugular vein where the blood is darker than that from an artery.
Because Sheila's arm would have been raised ( across her chest ) the blood from her neck would naturally have dropped onto her arm and run down the sides. Sheila would have to have been sitting up for this to happen.
I don't get where he says " the runs came to an end ". Of course they would if her heart wasn't pumping sufficiently enough for it to carry on running. Vascular shock leading to unconsciousness would have put paid to that.