If I lost my residency and I want to travel outside of the country would immigration give a permit to travel?

The permit would be to enter the country again....

Answer:
How did you lose your residency? If you've lost your residency and are still in the country, are you currently overstaying? If this is the case, and you have overstayed, if you then leave the US, there will be a ban put on you and you won't be able to enter back for 3-10yrs, depending on the situation. So no, you wouldn't be granted permission/permit to enter again. I don't know all your details, but try the link below, it has a lot of people who maybe able to help you out with advice. And you can find out what to do from an Immigration attorney.
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