How do Subject To Offers work for the seller? Won't the loan be called due?

[Arron Paulino]

Does someone mind explaining subject to offers? I ask as I have received offers from buyers that want to do an assumption of the current mortgage via trust acquisition and provide a down payment due to the seller. The terms would be a 30-day closing with a 10-day inspection period. 

Another offer is asking for owner finance for 84 months with monthly payments due to seller. Wouldn't the loan be able to be called due in this case or is there a loophole? Is there any way of reducing closing costs? Anything I should be aware of and counter with if needed?