If you're not already a US citizen first you must worry about how you will legally stay in the US after you drop out (your visa will be terminated). It is very hard to get a US Visa without a degree. One of our co-founders split time with school and our startup just so he could get his degree and pursue a visa. Make sure you know your full immigration status before you proceed. Immigration law sucks, do your best not to get caught up in it.
I wondered if F-1 or any other non-resident status allows you to own a part of a company or a profitable company. Could you please elaborate about that?
If you're really interested in this stuff you should contact a visa lawyer, email me and I can give you the name of a good one who will probably discuss your options with you for free. The following is just my experience, and not legal advice:
You don't have to hold any sort of visa to own a part of a company in the US. However, you cannot get paid legally (there are probably some exceptions with liquidity events) in the US without a visa and a social security number.
Some tricks involve setting up a foreign subsidiary that wholly owns or is wholly owned by the US company, then paying yourself as a consultant of the foreign company. This can work with UK companies, I can't speak for other countries though. Also, if you have such a foreign company that you can prove you worked for for a year in managerial capacity you can possibly qualify for an L-1 intra-company transferee visa.
The best route to a US visa is probably to stay in school. Don't worry about grades too much, but try to do things that get you recognition within the scientific community, maybe do some research and publish a paper or two. Basically, this is padding your resume for application for an O-1 (Alien of Extraordinary Ability) visa later.
One of the best options if you don't think you can qualify for that is to get a J-1 training visa. It is a very easy visa to get after you graduate and is good for 12-18 months depending on your prior work experience. You can then use this time to do things that push you closer to O-1 status so you can apply for that at the end of your J-1 or you can try and get lucky with the H1-B.
All of these things (except the L-1) require a US citizen co-founder who will fill out most of these forms and apply on behalf of you. In our company I'm that guy, so thats how I know all this stuff. Good luck!
