That's not entirely true...in four of the territories, the only thing they can't do is vote for president in the gener election or for the Senate; they can still send delegates to Congress, however.
They can send
non-voting delegates who are completely irrelevant. More importantly, they are U.S. citizens but they
do not have the same rights as U.S. citizens who are state residents.
As upheld by the Supreme Court in a series of decisions known as the "Insular Cases"; almost all of the Constitutional rights of the residents of U.S. territories are
overridden by the Constitutional authority of Congress to reign sovereign over federal territories. In legal jargon, the Constitution does not extend "ex proprio vigore" -- by its own power -- over the territories; Constitutional rights only apply
as Congress permits.
More specifically, the Insular Cases established that the Constitution only guarantees "fundamental rights" to territorial residents and not "political rights". SCOTUS did not explicitly enumerate "fundamental rights" beyond a generic invocation of life and property, but the following were explicitly established as "political rights":
1. Territorial residents are U.S. nationals but
not necessarily U.S. citizens. This is because the territories are deemed to be "subject to the jurisdiction" of the United States, but not actually
part of the United States. Under current law, Congress grants citizenship to persons born in all federal territories
except for American Samoa and the Northern Marianas; the residents of those two territories are deemed "non-citizen U.S. nationals". However, this is by grant of Congress rather than Constitutional right, and may be revoked as Congress wills.
2. Territorial residents do not have the right to
remain U.S. nationals. Congress has the power to "de-annex" any federal territory and strip U.S. nationality from its residents, at will. This has never been done in cases where citizenship had already been granted, but *has* actually been exercised for cases of "only" non-citizen U.S. nationals.
3. Territorial residents do not have the right to free domestic trade with the rest of the United States. Instead, Congress may tax trade between territories and states as if they are foreign countries. On the other hand, the territories are not
actually considered foreign countries and are exempt from "normal" foreign tariffs; they are only taxed
by specific Congressional levy.
4. Territorial residents do not have the right to trial by jury.
5. Territorial residents do not have Equal Protection Clause protections against discrimination; Congress is explicitly empowered to discriminate against territorial citizens.
---
On the other hand, SCOTUS has explicitly upheld the Fourth Amendment right against warrantless search and seizure as fully applicable
by right to territorial residents.
---
Obviously the forced cession of a U.S. state doesn't directly engage the territorial precedents, but then again,
nothing in American jurisprudence does, because it's considered unthinkable. It is, however, simply logical that Congress and the courts would base the cession of a state on the legal precedents surrounding de-annexation of a territory, this being the only thing in jurisprudence that is even vaguely similar. This being the case, there would almost certainly be lawsuits as to whether residents of the ceded state who entered the U.S. would be treated as foreign refugees rather than citizens, and the Constitutional outcome of those lawsuits is highly debatable.