What happens if soldier that has enlisted through MAVNI is being medically discharged?

Medical discharge is usually seen as being caused by circumstances beyond your control. Most benefits are intact with medical discharge. The exception would be the full GI bill, which requires 36 months of service. However you would still get the majority of your GI bill. Otherwise, if service is honorable, most other benefits will not be affected. Citizenship will not be revoked so long as you get an honorable discharge, which you should get in a medical discharge unless there is some allegation of wrongdoing on your part. See: http://www.uscis.gov/policymanual/HTML/PolicyManual-Volume12-PartL-Chapter2.html

The eligibility for most benefits is a combination of time served and your service characterization. If you are discharged medically, the characterization will be Honorable. Make sure that you carefully review everything and keep your medical records accurate and up to date. Please disregard any reference on their website indicating "Free Legal Advice". The information I provide does not constitute legal advice, but is offered only for general educational purposes. Any answer I provide does not create an attorney-client relationship. For legal advice, you must retain an attorney to work on your behalf. THIS ANSWER IS PROVIDED SOLELY FOR INFORMATIONAL PURPOSES

If you being medically discharged and are going through the MEB/PEB process, make sure your military disability(ies) ratings are full and complete as they have a direct impact on follow-on VA disability ratings.