The liver does do this with a substance called glycogen. It’s called counter regulation. It has a store of glycogen, which it will release into the blood stream

The liver does do this with a substance called glycogen. It’s called counter regulation. It has a store of glycogen, which it will release into the blood stream if BG drops too low. It is a finite store though, so if you exercise a lot (or overdose on insulin) you can metabolize most of it. In this case, hypos will become more severe and happen easier. Also, the store will be replenished by pulling excess glucose out of the blood over a period of roughly 24 hours after exercise or the hypo. So exercise has a beneficial effect of keeping BG lower for some time. That’s also why you should eat a little more and carbs after heavy exercise.