Ok this is really straightforward.
If Disney went Chapter 11, like the airlines repeatedly have, nothing would change at all. Their creditors would take over the company and continue to operate it. This is by far the more likely scenario.
But If Disney went Chapter 7, like Bed Bath and Beyond:
It’s important to note here that TWDC does not own
DVC. We do. They own DVD and BVTC. So new development would cease, and we’d need a new booking platform, but we’d still own our timeshares.
Now From the standpoint of amenities, there would be some changes. Obviously the assumption here is that the parks would close or be sold off. For the DVC properties themselves, the changes would vary greatly. Resorts that are entirely deeded to their owners like OKW and SSR would see minimal disruption - the owners would have to hire a new group to oversee housekeeping, the restaurants, lifeguarding, and boat rentals, but once that was resolved, you could still go, swim, eat, etc.
At the split resorts, it becomes really important what’s in the contract. At BWV the feature pool is part of the contracted amenities, and whoever buys the hotel side of BWV could not eliminate DVC owner access to Luna Park Pool. At Poly, however, owners are promised nothing. They’re entitled to whatever the hotel side wants to give them which the hotel side is allowed to change at any time. So you could literally have no pool and no dining.
So basically you’re looking at probably 2 months of disruption in services (including potentially booking, housekeeping and desk staff) while new management gets hired, followed by a whole lot of questions as non-DVC things get sold off.