Of course you may have structure issue when you modify the house without a building permit. Do you understand the process for permit approval? The problem new house have is not structural. If new house has structural problem either the architect or the builder has to go to jail.
Without the building permit, you don't know if the modification is done right. If you modify a load-bearing wall without calculation the load, you have the risk of collapsing the house. If you use the wrong wire gauge, or wrong breaker for your basement kitchen, you have the risk of burning down your house. If you don't put drainage vent for your basement bathroom, you have the risk of flooding the house....