The basis is Civil Code Article 717 (liability of the possessor and owner of a structure on land). In short: if a defect in the construction or upkeep of a building, fence or similar structure causes damage to someone else, the person actually using it is liable first. But if that person had taken the necessary care, the owner must pay instead. You can read the original text in the Civil Code on e-Gov Japanese Law Search.
In plain words: a "structure on land" is anything fixed to the land — a building, wall, gate, kura, barn, retaining wall. A "defect" is a lack of the safety the thing should normally have; for a house in snow country, that means a roof without snow guards facing the neighbour, rotten eave timbers, slipped tiles, a kura wall bulging and leaning. The "occupier" is whoever is actually using the building, such as the resident or the tenant.
Liability falls first on the occupier, then on the owner. If the occupier can show they took the necessary care, the occupier is excused and the owner bears it. The important point is that the owner has no such "I took care" escape route. Unlike the occupier, the owner must pay compensation even without any fault of their own. This is called strict liability.
In other words, "I live outside the prefecture and didn't know", "I only just inherited it and haven't been to see it", "I hired a management company to check on it" are not grounds for escaping liability. Hiring someone to check does not change who the owner is. Paragraph 2 of the same article applies the same treatment to defects in the planting or support of trees and bamboo: if a dead garden tree or a branch from a windbreak grove breaks the neighbour's roof, the mechanism is the same as for a building. Complaints about trees are covered in The neighbours have complained about an overgrown grove or garden trees. Paragraph 3 provides that where someone else caused the defect (such as the contractor who did the work), the owner who paid compensation can recover it from them.
What you owe is the damage suffered by the other party. In practice this is mostly property damage — a fence, guttering, a car repair bill — priced from a quote. But if someone is hurt, the figures change by an order of magnitude. Materials on vacant-house compensation cases published by Hino City, Tokyo, cite an estimate from the Japan Housing Finance Public Interest Foundation: ¥208.6 million where a vacant house collapsed onto a neighbouring house, destroying it and killing two occupants, and ¥56.3 million where falling exterior cladding killed a passer-by. These are not court awards; they are estimates prepared to show municipal staff the scale of damages involved. In short, the owner of a vacant house must pay compensation even without any fault of their own, and there is no upper limit on the amount.
"It was the heavy snow", "it was the typhoon" only holds where the damage could not have been prevented even with the safety the building should normally have. For a roof not cleared for years, or rotten eaves left as they were, expect it to be hard to argue. Beyond this, individual judgements are for a lawyer; we cannot draw that line. What we can do, as a building contractor, is see how dangerous the house is now and what would make it safe.