Little research has been completed on the subject of runners and core strength and no research could be found comparing core strength in fatigued and non-fatigued athletes. Athletes, coaches and specialists (such as personal trainers and researchers) alike all have very different philosophies about the importance of core strength and the most beneficial workouts.
Many arguments have been made that core strength leads to efficient movements and fewer injuries by stabilizing the pelvis and hips and allowing for an effective kinetic chain of movement (Fredericson, 2005). 
Ten college-aged female subjects with a mean mile performance time of 5:23 (+/- 43 seconds), an average of four years experience (+/- 2.73 years), a mean height of 66.22 inches (+/- 2.62 inches) and a mean weight of 129 pounds (+/- 8.82 pounds) performed three different tests (parallel arm raises, perpendicular arm raises and stabilizing) in the post-run assessment on the Lafayette Stability Platform. The platform measures when the subject moves the platform out of the center of balance and for how long they do so. The subjects completed the same three tests immediately following the workout in a fatigued state.
Statistical analysis revealed no difference in core strength between the fatigued and non-fatigued state. In the stabilizing test in which the subject balanced the board as steady as possible for 30 seconds, the subjects improved in the fatigued state and were able to hold the board steady longer for an average of .86 seconds. In the parallel arm-raising test in which subjects raised their arms every second as marked by the metronome, they also improved on average by .26 seconds. In the perpendicular arm raises the subjects declined an average of .08 seconds. A low correlation in core strength and performance time (r = .138) was determined.