My rough estimate would be that if blood pressure reaches 35, then this is a very critical stage.
How low can blood pressure go?
Blood pressure is measured through two figures: Systolic pressure (the pressure in your heart) and diastolic pressure (in your arteries).
Something like 61/38 would be a seriously low BP that would require emergency medical attention.
If either systolic or diastolic pressure drops much below 30 then I would expect death to be imminent.
Low blood pressure (or hypotension) occurs when the blood in your arteries isn't pumping around with enough pressure to reach your brain and vital organs properly.
In terms of "how low your blood pressure can go" before death, it really depends on which organs are being deprived of blood, and how dramatic the drop in pressure has been.
A sudden drop (due to things like uncontrolled bleeding, infection, or allergic-reaction) could prove fatal.