They come to the U.S. to train for the mission of safeguarding their country, but Afghan soldiers often decide they don't want to go back.

On Monday, a trio of soldiers, here for a wide-ranging training program that has been in place for a decade, was caught at the Canadian border after disappearing from a base on Cape Cod Saturday. They were just the latest group of Afghan soldiers to try to melt into the North American population. While authorities have not said what their motive might have been, AWOL Afghan soldiers have previously sought asylum, claimed to be merely sightseeing or simply never been found. So far, none has posed a terror threat, according to officials

"There is a lot of speculation within the military that they may be trying to defect," Massachusetts Gov. Deval Patrick said of the three who were found Monday.

Since 2004, soldiers and pilots from Afghanistan and other nations have taken part in what are known as Regional Cooperation training exercises to promote cooperation and interoperability among forces, build functional capacity, practice peacekeeping operations and enhance readiness. And with the U.S. drawing down troop levels in Afghanistan, the program is crucial to getting Kabul's defense ministry more self-sufficient.

This year's exercise, which involves more than 200 participants from six nations including the U.S., is scheduled to wrap up Wednesday. There are about a dozen more Afghan soldiers still participating in the exercise. Military officials from Tajikistan, Pakistan, Kazakhstan and Mongolia are also participants.

The latest case came just days after two other Afghan military trainees vanished from a Drug Enforcement Administration training program, only to resurface in Buffalo, where they told authorities they’d gone on a sightseeing road trip. DEA spokesman Rusty Payne told FoxNews.com that those men were never considered a national security threat and will be be returning to Afghanistan as planned. He said the two were part of a group of 31 Afghan officers who had traveled to the U.S. to participate in an intensive anti-drug trafficking program with the DEA in Quantico, Va.

A U.S official told Fox News that situations such as these happen “frequently” when the U.S. military brings Iraqi and Afghan troops and officers into the U.S. to train. Typically, the foreign nationals are seeking a better life for themselves, the official said.

Just last week, during the NATO summit, an Afghan colonel arrived at the Embassy and asked for asylum. He was denied asylum and told he would need to return to Afghanistan. And in 2010, FoxNews.com broke the story about 17 members of the Afghan military who were training to become pilots and learning English disappeared from a Texas military base. Most were eventually located, but a few are believed to have melted into the Canadian population. Afghan soldiers have been known to mount surprise attacks on their U.S. counterparts, killing dozens stationed in that country, and the Pentagon cannot guarantee its claim these men don’t pose a threat. But they say the ones brought here for training undergo extensive vetting and are believed safe.

Pentagon official Major Andrew Aranda said those chosen to come to the U.S. for training are carefully screened with polygraph testing and other methods as part of the "Leahy vetting process."

"They're not a threat," Aranda said. "They were invited by us, by the United states, to participate. We invited six nations to participate in the exercise to promote cooperation throughout the region.

"They were vetted," he continued. "They're considered foreign delegates holding passports with valid U.S. visas and the visas are granted through the U.S. State Department using the Leahy vetting process."

The level of monitoring depends on the type of training the foreign nationals are here to undergo, according to U.S. officials. If they are emerged in "a more open classroom environment," it is "on their own integrity to show up to class," said one U.S. official.

Retired U.S. Army Lt. Col. Ralph Peters, a Fox News contributor, said it isn't so surprising that Afghan soldiers would prefer to stay in the U.S. than go home, and said the latest example is typical.

"These guys were not a threat," Peters said. "They were would-be deserters who wanted to spend the rest of their lives shopping at Walmart, not the Kandahar bazaar. We may believe in the Afghan military, but these carefully vetted officers clearly don't."

Fox News' Cristina Corbin, Jennifer Griffin and Jana Winter and The Associated Press contributed to this report.