How would Texas handle federal crimes that happened before independence?

These are handled in the transition, under rules set in the separation agreement, and sorted by what the offense actually is. The honest, simple answer is that pre-independence federal cases do not disappear and do not get dumped. They are wound down or transferred, the same orderly way every other in-progress federal matter is handled.

Most "federal crimes" are also crimes under Texas law

Start with a fact that shrinks the problem. The serious conduct people picture, violence, fraud, trafficking, theft, is already criminal under Texas law as well as federal law. So for the large majority of cases, there is a natural Texas home. Conduct that violated both federal and Texas law can be prosecuted in Texas courts under Texas law, where the offense was a Texas offense all along. The category of conduct that is somehow only a federal crime and has no Texas analog is much narrower than the phrase "federal crime" makes it sound.

Cases already in the federal system get sorted in the transition

For prosecutions and investigations that are in progress when independence takes effect, the separation agreement sets the rules, just as it does for pending civil cases and for people already in custody. A matter rooted in conduct that is also a Texas crime can be continued in Texas courts. A matter that is purely federal, or one in which the United States is the injured party, can be completed in the remaining U.S. system or resolved as part of the separation terms. The principle is continuity: nothing is dropped, and the handling of each case is agreed in advance rather than left to chance.

The line nobody crosses: independence is not a get-out-of-jail-free card

Let us be plain, because this is where the real worry lives. Restoring Texas independence is not an amnesty for criminals. A person who committed a serious crime does not escape accountability because the flag changed. The transition is designed precisely to prevent that, by ensuring every genuine offense has a forum, whether that is a Texas court for conduct that is also a Texas crime or the U.S. system for matters that remain federal. And where a fugitive tries to cross the border to dodge justice, the extradition treaty between Texas and the United States, described in its own question, closes that door in both directions.

Conduct that was never wrong in Texas is treated honestly

The flip side matters too, and a rule-of-law nation handles it honestly. International practice on extradition turns on dual criminality, the idea that a person should answer only for conduct that is a crime in both places. An independent Texas would apply that same fairness principle to the narrow set of purely federal offenses: it would cooperate on genuine wrongdoing while not treating Texans as criminals for conduct that was never an offense under Texas law. That is not a loophole. It is the basic justice principle that you answer for crimes, not for things that were lawful where you live.

Texas has the courts and the law enforcement to do this

As with every part of the legal transition, Texas is not improvising the capacity. Texas courts of general jurisdiction can try any offense under Texas law, and Texas law enforcement already investigates and prosecutes the full range of serious crime. Handling pre-independence cases that belong in Texas is work the Texas system is already built to do.

The bottom line

Pre-independence federal cases are handled in the transition, sorted by what the conduct actually was. Most serious offenses are Texas crimes too and can be tried in Texas courts; purely federal matters are completed or resolved under the separation terms; and an extradition treaty stops anyone from using the new border to escape. Independence is not amnesty, and it is not a vacuum. It is an orderly handoff.