So, nobody's really talking about it (or if they are, it's buried in DRM salt), but I think the old man is dead. Or at least was prior to the reset. Or maybe nobody's talking about it because it was obvious to everyone else.
1) Tsuneyo's reluctance to the ramen shop is unusual. Like there's something she's trying to avoid.
2) She's being morbid in the scene on the bridge, even asking (obliquely) about what will happen to her.
3) She's genuinely afraid to to go to the shop.
4) She's later called to the shop by her neighbor because of a smell.
There's nothing concrete, but I think she suspects that he's gone, and is afraid to return to the shop because that would make it real.
It also helps that she was talking about the potential for rain, and my brain IMMEDIATELY jumped to Hughes' funeral in Fullmetal Alchemist. That might have seen me down the Red Herring Trail, actually.