The warrant will continue until the minor, now adult, eventually takes care of it or gets picked up on the warrant. I've had cases where juveniles were already 20 years old and were picked up on a warrant. This person should consult with an attorney.
As my colleague stated, the warrant will not go away. The reason is that a warrant is a directive to law enforcement to return a person to the court. The arresting agency does not have the authority to decide whether a warrant is valid, or timely, etc. Those issues must be resolved by a judge.
Practically speaking, if a person is no longer a minor, it would be pretty counterproductive to send him to a long-term custodial juvenile facility to punish him for running away. But the court is a good forum to identify what services are still available to the now-adult, such as education, shelter, etc. Understand that my opinion that putting the 18-yr old back in long-term custody would be "counterproductive" is just that: an opinion. Judges do all kinds of squirrely things. That is why it is especially important that the 18 yr old who finds himself in this position have an attorney who will advocate vigorously to get the kid the social services, etc. he needs, as opposed to a jail cell.