What would happen during the American Civil War if someone living in the Confederacy was conscripted but loyal to the Union?

Let’s say they were conscripted but were loyal to the Union instead. Would it be realistic for them to escape and go north? If they flat out said they were union loyalists, how would the Confederate military treat them? I assume they were jailed or possibly executed. Did this happen? Could they have chosen prison instead or was it train or be killed?

Would it have been realistic to surrender to the Union and explain to them they were conscripted but loyal to the Union? How would the US military react to this? Did this happen? Could they have joined the Union army after this situation occurred or would they have not allowed this due to spy suspicions?