Q.How prevent mold and fungus to enter a broken plant
How do you prevent mold and fungus from entering a severed stem when using the process of grafting?

It depends upon the plant or shrub you are grafting. For trees and shrubs the grated area can be sealed with a tar like product called Tree Wound Sealer that is available at some hardware stores such as Ace Hardware and some garden centers. It can be messy to work with but does its job well. In other cases once the graft has been made and is temporarily held in place, the entire grafted area can be sprayed with a good fungicide such as Green Cure or Immunox, let dry and then the final graft protection wrap/covering applied. The final wrap area can be sprayed again as well. This early spraying gives the graft a chance to get set and truly take before any fungus can even think about making an attempt at an attack.