Nothing happens as there is no blood being produced. The hormone in the IUS has puts the lining of the uterus (the endometrium) into a resting phase.
Monthly menstruation is simply the lining of the uterus – which, as part of the normal menstrual cycle, has been stimulated to grow in preparation for pregnancy – which comes off. But, with the IUS this lining is not stimulated to grow – so there is no "blood" or lining to come out.
Think of it the same way as in the winter when the grass doesn't grow – there is no need to cut it. And just like the winter grass doesn't disappear and grow back into the ground – nothing untoward can happen if you stop having monthly bleeds because you are using the IUS. This is a big issue for women to get their heads around as many people still buy into the myth that a monthly bleed represents a "cleansing". This is not the case and it is not unhealthy if you do not have a period because you have the IUS in. There is simply no bleeding because there is no uterus lining to come off and bleed away.
When the IUS is removed, the endometrium will start growing and periods will return.