They do call this country, the United States of America, for a reason, and that reason is that the United States of America is a confederation of fifty separate States. Although, over the years, the Federal power and might has continue to increase often at the expense of specific State rights, there are many instances to which State rights and laws are the meaningful sovereign power within that particular State. For instance, bench warrants for arrests are issued all the time, typically for things such as missing a court-mandated appearance or for failure to comply with court-mandated orders, or such similar things, to which the charge must be answered within that particular States' borders and court system.
However, like many things, there are exceptions to the general warrant for your arrest rule, and the very basic exception to the rule, is that an arrest warrant issue by one State judicial system must be executed within that State. This does not mean that the arrest warrant is invalidated by simply moving from one State to another, but it does mean, that for the most part, should you have an arrest warrant, for example in Florida, but you currently are residing in Texas, that unless that warrant is for a specific crime that piques the interest of Texas authorities, they probably will not take any action against you in the State of Texas in regards to the particulars of your Florida arrest warrant.
It isn't that an out-of-state arrest warrant can't be acted upon outside the State it occurred in, because legally it can, what it does mean often though is that it won't be. Basically, an out-of-state warrant can result in your being arrested and place in jail, pending rendition to the State that has issued the warrant, but in most situations this won't actually be done. So whether you are unaware of an out-of-state arrest warrant or are quite aware of the warrant, the moving of your person from one State to another State, will, often in effect, preclude you from having to appear in court to answer said warrant.
Of course, having a warrant for your arrest, is definitely a problem that should be addressed, and the removal of your person from one State to another, does not actually take care of the problem, it merely, sidesteps it. So that, all things being equal, once you become cognizant of the arrest warrant, legal counsel should be engaged so as to rectify the situation in a manner that is most favorable to you, or at a minimum, to at least get a better understanding of what you are up against and the ramifications of it.
Most people are unaware of how bad missing a mandated court appearance or failing to adhere to court mandated terms can be to an individual, as often, the judicial response to these sort of matters, is to issue an arrest warrant, maybe not so much as to punish you, but in effect, to compel you to answer in a court of law to the charges that have previously been addressed against you. The fact that the arrest warrant has been issued in a different State will often give you breathing room, but will not negate the warrant itself or its validity.