Is it OK to ask for deferral of graduate school admission because one has failed courses to make up? What would happen if a student was admitted to graduate school (only consider US institutions here), but failed a course later and would have to wait till the next time to take the course to make up for it and get the bachelor degree? 

Do they have a chance in this situation to apply for a deferment of admission for a fraction of a year?
I suppose it's okay to ask.  But since graduate admission is generally contingent on successful completion of your undergraduate degree, I think it's much more likely that the graduate institution will rescind your admission.  You would need to make a fresh application in the next admission cycle, with no guarantee of acceptance, and the failed course would tend to weaken your application.