If a person is in America illegally can they get on an airplane with their Mexican passport and leave to Europe where they will leave legally without intentions of coming back?

To be able to legally reside in a country you have to get a resident visa. If you have a legal passport you can get on a plane going anywhere. However to get through customs at your destination you will need some sort of Visa.

The US will not question how this person got into America? Only the country where the final destination is will want proof of a resident visa, correct?

If the person has a valid passport and is leaving the country, they will not question how they got into the country in the first place.

I may disagree, since they are not a US citizen, they will have to go though immigration and they will question why there is not a valid VISA to be in the US. They may be detained and questioned as to how and why they are in the US. They may be allowed to leave but immigration does have the right to detain.

I may disagree, since they are not a US citizen, they will have to go though immigration and they will question why there is not a valid VISA to be in the US. They may be detained and questioned as to how and why they are in the US. They may be allowed to leave but immigration does have the right to detain.

U.S. does not have exit checks, either at land borders or at the airport.

I may disagree, since they are not a US citizen, they will have to go though immigration and they will question why there is not a valid VISA to be in the US. They may be detained and questioned as to how and why they are in the US. They may be allowed to leave but immigration does have the right to detain.

There is no exit check. TSA officers only want to know what are in the person's carry-on, not the status or how that person entered US. All airlines must report passengers info to DHS.

In conclusion, if you live in US illegally, you can leave any time, no problem.

What happens in customs at the other end is another matter entirely. You don't just hop off the plane and go your merry way, living there forever.

If you plan to go to Europe you'll need to have all your ducks in a row. I'm a landed immigrant in Canada. I'm actually a German citizen. I've never had issues leaving Canada to go to Europe, but getting into Germany, even though I'm a citizen, is not always easy, even when I'm only going for a visit. Leaving is even harder, and getting back into Canada, after only a 3 week visit to Germany, is not fun, even though I'm a legal resident in Canada.

You're not a legal resident in the US, or Europe. You may not have a problem leaving the US, but good luck getting into Europe without a visa.