Granting TPS to Haitians is a small silver lining in the devastation that is occurring in Haiti. I lived in Haiti in 1997 and this is just heartbreaking. I hope you and your family have been spared.
TPS will allow you to stay and work legally in the United States for as long as the US Congress will renew the status for Haitians. However, TPS alone will not lead to legal permanent residence. You can explore other options for obtaining legal permanent residence while you are on TPS.
If you have been here for more than 6 months without valid immigration status, you should talk to an immigration attorney before leaving the US for any reason. You may trigger a 3 or 10 year bar on returning to the US once you leave and then try to come back in.
Please be sure to file for TPS on time.
I strongly advise consulting with an immigration attorney before filing any papers with immigration, particularly if the person for whom you are filing has any past negative immigration or criminal history and is in the United States. There is always a risk of removal from the United States.
Good luck to you.
Sole Member and Attorney
The Bortel Firm, LLC
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Minneapolis, MN 55415
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Note: The above answer is provided for informational use only. One should not act or refrain to act solely based on the information provided. No attorney client relationship is created unless a retainer is signed by the attorney and the client.