|I can empathize with Jonathon. As an oldster in the making I too like my things around me, and don't like strangers touching my stuff either. You asked for some constructive overhaul, so here it goes.
In the sentence below change (any stranger) to(and strangers) in the other( ) put the word (the)
She didn't understand that he needed his things around him; (any stranger) wouldn't have( )proper respect for them.
In the paragraph below you have him opening the door twice. Also how can he open the door if he is leaning on it?
Reaching his destination, Jonathon opened the fridge and with a shaking, bony hand, withdrew another beer, the generic kind he used to despise. He leaned against the fridge door to open it and take a long deep drink, and as he lowered it he began to rasp again and was forced to set the beer on the grimy floor to wipe his mouth.
Maybe you could say:
Jonathan leaned against the fridge, and with a shaking, bony hand, opened the door and withdrew a beer, the generic kind he used to despise. After taking a long deep drink, he began to rasp. He lowered the beer and placed it on the cluttered table, and proceeded to wipe his mouth with the back of his grimy sleve.
Now the events follow a logical procession.
Also I changed him putting the beer on the floor to putting it on the table. If he is old, sick and feeble it would be difficult for him to bend down that low and then get up again. I know it is difficult for me with my arthritis, and I will only be sixty in the next couple of months. I also have him wiping his mouth on his sleve, he must wipe it on something maybe you can give him something else to wipe his mouth on.
In the next sentence (faces) need not be capitalized
Seemingly kind (Faces) turned ugly
I would combine the next two sentences. A sentence should have a noun and a verb. (But enough) doesn't have either. I would also add the word (did sell.) after enough.
Not much sold at the auction, he'd been told, when it all went up on the block. But enough.
I like the last two lines but it doesn't really seem to fit quite right. You said that he was popular but you don't mention why or what was so special about this lonely old man. He probably outlived most of his friends and fans. Why would he need a nurse or a cleaning lady if he had any family that visited. He wouldn't mind family touching his things. You need to tell more about this man to get the reader to even like him or want to know more about him or even feel something for him. Those last two lines seemed to be put there for the soul purpose of ending the story. There is a lot of potential in this story. You should unfold the mystery about this man it would make it more interesting to read. I hope I didn't overstep my bounds but you asked for a constructive overhaul. The descriptions of his dreams is nicely done but you don't tell why he is having this recurring dream. what happened to him in his past that is causing them. There has got to be something more to this man than meets the eye. I hope I have helped in some small way. Ginger