They are a parasite, even though they are part of the corn plant. Everyone in this area calls them "suckers" because they "suck" the nutrients away from the main corn plant and rarely produce anything viable. Many do let them grow because they don't have the time to pull them in a large garden. They will just add a little extra fertilizer to feed the main plant. Sometimes I will walk through my corn and pull the larger ones so they don't drain the nutrients away from the main plant.
I have never heard of them helping to stabilize the main plant. It could be true, but I believe they are much more detrimental than helpful. For corn to have good solid roots it needs to be slightly
water stressed occasionally while it is growing so the roots will go deep looking for moisture.
Another way to help stabilize corn is to "hill" it. Pull dirt up around the stalks from between the rows anytime it is big enough that you don't knock it over while doing it. My Troybilt tiller has a hilling/furrower attatchment. It can dig a trench up to 7" deep between the rows and piles all that dirt up around the stalks. The corn has to be 2'-3' tall to put that much dirt around it. I can set it shallower if I want to hill it sooner.