I attached the simplest model that breaks. Here is the code inside "Conditional Delete". It will not even start if the feature class doesn't exist, but the whole point of the script is to see if the feature class exists first.
import sys, os, arcpy
# Get the input from the model
InputFC = arcpy.GetParameterAsText(0)
# Statement to check the existence of the feature class
if arcpy.Exists(InputFC):
arcpy.AddMessage("Feature Class Exists and will be deleted!")
arcpy.Delete_management(InputFC, "FeatureClass")
arcpy.SetParameterAsText(1,"True")