Mine stand up against the closet wall for the most part. Would think that cases are designed to be flat as if you were opening them. Neck would have more support etc. I always take a little tension off the strings if I am going to leave one in the case for long and a humidifier is a really good idea too , fretboards will dry and fret ends become painful.I installed a humidifier in my house system and try and keep it above 50%. I have seen many that say don't leave on stands/hangers but I can't see the issues there either ? I have pulled guitars out of cases that were in them for 20 years and it can be ugly , if tension is left on , the neck can pull way up.