What happens with the nitrogen in blood in membrane oxygenators?
It gets diffused out, like you expected.  Grist (2013) writes about this in relation to &quot;the bends,&quot; which has already been mentioned by user1136.  He writes:

Cavitation of blood containing normal oxygen and nitrogen levels by mechanical heart valves after implantation generates bubbles that can be detected in the brain using transcranial Doppler ultrasound (2). These bubbles are mainly nitrogenous. Nitrogen is less soluble in water than oxygen. So during excessive turbulence, temperature changes, or pressure changes, nitrogen is the first gas to come out of the solution. (Ask any knowledgeable diver about the physiology of the bends.) We know these bubbles are mainly nitrogen because when the nitrogen in the patient’s blood is off-gassed by breathing 100% oxygen, the cavitated bubbles go away. In one study, the administration of 100% oxygen by facemask reduced the cavitation generation of GME by 98% (3). [Emphasis added]

Can't say it a lot better than that and the rest of the article.  When people are breathing de-nitrogenated air, it simply results in nitrogen being diffused out of the blood.  So yeah, basically the amount of N2 goes down to 0, at least if they are on it for long enough.
As for it being bad for you, not really, at least not perceptibly: though nitrogen is critical for body function, it's practically useless to the body in the N2 form; it has to be &quot;fixed&quot; to a more reactive form such as ammonia / other nitrogen oxide.

Sources

Grist G. 2013. Oxygen or Nitrogen: Which Is the Lesser of Two Evils? J Extra Corpor Technol 45(1): 61-63.

Sprent JI, Sprent P. 1990. Nitrogen fixing organisms: Pure and applied aspects.