Essential tremor is due to a genetic
defect and can be inherited.
Breathing and heart failure can cause
brain damage because of the hypoxia if it
lasts long enough. Brain damage can be
manifested with tremor, but such tremor is
not called "essential" but "symptomatic",
which means it is due to some other
disorder (in this case - brain damage).
Can you give me some more information
regarding this person's medical history?