Story highlights Alberto Morales, 42, was shot early Saturday

He escaped from custody Monday, after allegedly stabbing a detective

Authorities tracked Morales to a wooded area near where a home was burglarized

Authorities in Texas shot and killed an escaped prisoner early Saturday, several days after they say he stabbed a detective tasked with taking him across the country.

Alberto Morales, 42, was killed shortly after he was located in a wooded area in Grapevine, near Dallas, said Grapevine Police Department spokesman Sgt. Robert Eberling.

With the help of a helicopter, authorities found Morales not far from a home where someone stole jewelery and men's clothing.

"At this point, as far as the investigation is concerned, Mr. Morales was shot and is now deceased. This matter is still under investigation ... and we'll have more details at a later point," Eberling told reporters.

He declined to say whether the escapee was armed and did not elaborate on the circumstances surrounding Morales' death.

Eberling stressed the case remains under investigation.

Morales' death ended a manhunt that began on Monday. It was then that police say he stabbed a Florida detective multiple times and disappeared. That detective, and another, had been transporting Morales from Florida to Nevada. The trip began on a Miami-Houston-Las Vegas flight.

Prior to landing in Houston, Morales began "acting erratically," according to a statement from the Miami-Dade Police Department. As a result, he and the detectives were not allowed to board their connecting flight, it said.

The detectives rented a vehicle and continued on their way, making a pit stop in Grapevine to use the restroom. While one of the detectives was inside, Morales stabbed Det. Jaime Pardinas, a 28-year veteran, multiple times, and fled the scene, authorities said.

Pardinas was treated at Parkland Memorial Hospital in Dallas and was listed in serious condition, the statement said.

Morales was arrested in Nevada in 2008. He was brought to Miami, where he was jailed pending a 2003 case alleging burglary, kidnapping and sexual battery. In December, he pleaded guilty and was sentenced to 10 years in prison, which was to run consecutive to a Nevada sentence.

Details of Morales' Nevada case were not immediately known.

When asked by a reporter how authorities felt at the conclusion of the manhunt, Eberling said he was relieved for local residents.

"We knew we had a dangerous individual out there in the streets. And he was capable of being extremely violent. So that is what we're relieved of. The fact that Mr. Morales is now deceased is not something that we celebrate, but our jobs is to apprehend the fugitive," he said. "It is a relief to this community and I think a lot of folks in this area can now have a moment of rest."