Could you please explain the process after an investor obtain an EB-5 visa? Does he need to leave the U.S. after a certain period of stay? Can he stay indefinitely with this visa?
Upon being approved for an EB-5 petition and adjustment of status to a lawful permanent resident, you can remain/work/live in the U.S. indefinitely. The only condition is that you file for I-829 removal of conditions of permanent residence within two years of being approved for lawful permanent residence under EB-5, with evidence of business, requisite job creation, etc.
When you get EB-5 visa in your passport, you need to arrive in the U.S. within six months of its validity period. When you arrive, you become a conditional permanent resident (with a two-year green card). You need to remove conditions to get 10-year green card within 90 days of the expiration of your two-year green card. You may apply for U.S. citizenship within 90 days of expiration of five years since your initial green card date, assuming you meet all requirements. If you intend to stay outside the United States for a period longer than one year, you must apply for a re-entry permit that will allow you to be outside the U.S. for up to two years or validity of your two-year green card (whichever is shorter). You must still maintain ties to the U.S., demonstrating it is the country of your permanent residence, such as having a home or apartment, family in the U.S., assets in the U.S., filing U.S. taxes, children registered in U.S. schools, etc.
Once your EB-5 visa is approved, then you receive a two-year conditional green card that allows you to stay and live in the US. As a green card holder, the U.S. will be considered your primary place of residence. However, you are free to travel outside the U.S. as long as you don't stay out for more than six months, unless you apply for advance parole. That would allow you to stay longer. Then, three months prior to the expiration of your conditional green card, you must apply for removal of conditions from your green card by filing the USCIS Form I-829 to obtain your permanent green card.
I am assuming you mean legal permanent residency (LPR) or a green card! You can stay, work and live in the U.S. for as long as you maintain your green card status. In other words, while you are on LPR status, if you commit a crime, sometimes a minor crime, you may lose your status! You can travel outside of the U.S., but for no more than six months at the time.
With the EB-5 visa, I assume you mean obtaining your two-year conditional green card. As you know, the step before that is the filing of your I-526 petition. The approval of this petition allows you to apply for the conditional permanent residency but in and of itself, does not grant you the right to live and work in the U.S. Until you get the conditional green card, you would need another visa, such as F-1, B-1/B-2, H-1B, E-2, etc., that grants you the right to be in the U.S. lawfully. Once you obtain your two-year conditional permanent residency, you are expected to be in the U.S. Ninety days before the expiration of your two-year conditional permanent residency period, you are allowed to apply for the removal of conditions through filing the I-829 petition. That filing will automatically grant you another one-year extension of your conditional permanent residency status. This lawful residency status will remain in effect until your I-829 is adjudicated.
After an EB-5 investor obtains an immigrant visa and is admitted to the U.S. as a conditional permanent resident, he needs to be in the U.S. periodically in order to maintain his conditional permanent residency. He can stay indefinitely in the U.S. in such status. He can also depart periodically, although it is advisable not to be out of the U.S. for any continuous period longer than six months. Approval of the EB-5 petition by itself does not give one the right to enter the U.S.