Strays were rogue programs who lacked identity discs. During the rule of Clu, they would be rounded up by Guards and Sentries to be rectified.
Strays often lost their memory in fits called glitches after being parted from their disc for too long. These glitches often provoked the victim's vision to blur or stay out of focus until the program experiencing it regained their sense after a while. A stray later forgets their own identity and memories after experiencing several glitches.
History
1989
After having his Identity Disc stolen by local theif, Galt, Beck was believed to become a stray after some time. Beck and his mentor, Tron, headed to the original settlement of Argon City, Purgos, to re-obtain his Identity Disc.
During the period before he re-obtained it, he constantly was in a state of instability. Tron warned Beck that permanent amnesia would set in after prolonged separation from his disc, causing him to not even know his own identity. It was later revealed that Kobol had kept Beck's identity disc and that he was planning to hand Beck over to General Tesler once he fully became a stray. Tron prevented this and when Beck regained his disc, he was able to download his memory back and the glitches stopped.[1]
2010
After entering the Tron system, Sam Flynn, the son of Kevin Flynn, was abducted by Sentries under belief he was a stray due to his lack of an Identity Disc.[2]
Other mentions
Kingdom Hearts 3D: Dream Drop Distance
Like Sam Flynn, Riku and Sora were also abducted under belief of being a stray in Kingdom Hearts.