No they don’t.
Corns on the feet do not have roots that they grow back from after being removed like some garden weeds do if you do not take out the roots. Corns are caused by a reason and if that reason is not removed, then the corn will come back again regardless if it was debrided by a podiatrist or you tried a corn remover pad. If comes back for that reason and not because there is a root there for it to grow back from. If you want to permanently get rid of corns, then that reason it is there has to be removed.
The “reason” for a corn is almost always too much pressure on an area, so that the skin thickens up to protect itself. It then becomes too thick that it hurts – that is what a corn is. To get rid of a corn, you need to identify what is causing that excessive pressure and find a way to reduce it. If that is possible then it will stop coming back after being removed.