Assuming you’re not dead, of course. 
But some guy was telling me he once had a BP measured at 158/0 when he suffered from heatstroke. My first reaction was to cry “bullshit”, but then I thought to check the SDMB first…just to make sure.
Diastolic BP is measured, when using a stethoscope, by a change in the sound. It can be missed with heat stroke, because the heart is trying to compensate by beating harder and faster, so the quality of the sound change is minimal.
Also the outside noise at a rescue scene can effect how well the rescuer can distinguish the sound change.
Usually, when a diastolic pressure can’t be heard, the BP is taken again while feeling the wrist pulse. the reading is then recorded as ***/palp, which means palpation.
So the answer to you question is no, one can not have a diastolic BP of 0. But the diastolic pressure may not be measurable.
Tibetian monks can get their pulse down under 10, so maybe Dalai Lama could tell you the answer.
Pulse and blood pressure are not the same thing.
It is possible to get a diastolic pressure of 0, especially in types of shock. Blood pressures are measured in millimeters of mercury or mmHg. Essentially that’s like saying if you were to hook a pressure meter with a column of mercury into an artery in a normal person it would go to 120mm during the time the heart is beating (systole), and to 80mm during the time the heart is resting (diastole). This pressure is a function of the diameter and complicance (stretchiness) of the artery (i.e. it’s higher in old people with stiff arteries. As such, in some instances, it’s possible for the body to dilate it’s blood vessels to the point that when the heart isn’t beating there is no measurable pressure.
USCDiver
T-20 days to MD
Of course there would be no blood pressure if the heart isn’t beating!