Interesting they didn't use the original holes for the replacement neon.
As to why the place likely went under, it's all but impossible for a single screen theatre to survive these days. Actually, it was almost impossible even 30 years ago when so many were closing. It's hard to get film. The investment for modern projection/sound is high (even the move from carbon to xenon lamps which didn't happen here and forget about the move to digital).
You also saw a lot of cases where the owners got old and retired/passed and there was no one who wanted to take it over. It was a lot of work and after the 50's - 60's it wasn't easy to even break even. You saw a lot of older couples running local theatres as their retirement hobby...
The cardboard must have been put there after it closed or when some final maintenance (like oiling) was done. Cardboard there when the lamp is running would have been burned within seconds.
I know we all hate to see this kind of equipment rotting away. While old theatre seats and similar customer facing items have value, old projection equipment is essentially worthless. There isn't a single item here that would be of any use to a modern (or even less than modern) theatre. Most of that equipment is so heavy it isn't even worth hauling out for scrap prices.
As a lover of old movies I also have an interest in the old movie theaters. This should be interesting. I'm already liking that this and other pictures in the gallery look so colorful. Anyone remember the early years of the AMC TV network? They showed grand movie theaters very often, but not if they were in bad condition. The network has since changed formats and gone way downhill since then. But at least they have The Walking Dead!
Amazing that back in the day such architecture was seen as beautiful aesthetic, wealth and prestige as though the patient's were in good hands and well looked after. Now we identify it as something different; something somewhat vulgar, macabre and haunting. It's funny how values change.