If you have an smaller window on front of FFXI window (don't matter if it's SE window mode or windower) and you click to minimize or click within the game window to change focus to FFXI, that odd behavior usually kicks in. It's due to the fact that once the focus is back to FFXI, the game pad does not work for a second, but the mouse and keyboard work instantly.
The game then picks the mouse button still pressed from the previous application (as you didn't release the mouse button yet) and locks on auto run mode.
Quick fix is just click both left and right buttons on the mouse twice.
The character will then stop walking.
Edit: To prevent that from happening, refrain from clicking within the game active area and instead click the title bar or the game button on the task bar.