Greg, I found this definition of furlough at http://www.civilwarhome.com/terms.htm. It states that the soldier had to turn in his arms and accoutrements, ie sabre probably. So, unless the soldier had personal firearms, he would have been travelling unarmed.
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Furlough - An enlisted man's leave from the Union or Confederate army, granted at his superior's discretion, was called furlough. Rules in both services specified that furlough be granted by a commander actually quartered with the soldier's company or regiment. A furloughed soldier's arms and accoutrements remained behind, and he carried furlough papers giving a detailed description of his physical appearance, return and departure dates, unit designation, and pay and subsistence allowances furnished. Furlough papers warned the soldier to rejoin his unit by the date specified "or be considered a deserter."

Furloughs differed from leaves of absence. Officers were granted leaves, whose rules and stipulations were more extensive. Both leaves and furloughs were freely abused, and both armies had occasion to cancel all leaves and furloughs to account for deserters and malingerers. They were also used as inducements: on expiration of enlistment, entire Union army regiments were given "veterans furloughs" if they reenlisted. There were for an extended time, allowing soldiers to return home, and accounted for a dramatic increase in the national birth rate 1863-64.
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I looked this definition of furlough up because the Union soldiers on the train stopped in Centralia, MO, were all unarmed according to descriptions. That would account for why they could not put up a fight when Anderson's men attacked the train. Deborah who is corresponding with me about our Thomas and Pace relatives both being killed there showed me in an email where her Pace ancestor's application for child's pension was denied in 1864 or so. Reason, soldier had been "discharged." This was not true, he was on furlough. Pension was resubmitted in 1877 along with a statement by witness Thomas Goodman. It was approved that time.

My Thomas ancestor's wife and children applied for but did not receive pensions either. I've found the documentation showing the request numbers but no certificate numbers and no explanation why not. I'm wondering how to find out why. I have his "Final Statement" clearly showing that he was killed 27 Sep 1864 at Centralia while on furlough.

Current definition of "leave" means the person is still on active duty, just on "vacation." I'm 20 year Air Force vet, had 30 days furlough/leave annually, just like back during the Civil War. Paper was signed by the squadron commander too, just like during the Civil War.

Tom