Diastolic pressure less than 60 mm Hg is generally considered as hypotension,
Severely low blood pressure can deprive the brain and other vital organs of oxygen and nutrients, leading to a shock.
In general, DBP shouldn't get below 35-40 mmHg - this is the filling pressure needed for the coronary arteries to perfuse.
No coronary perfusion, of course, is a very bad thing.
Symptoms may start before this point however, especially if you normally are hypertensive, so I'd start getting concerned once your DBP gets below 55 or so.
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