As far as the other dog surviving, it wouldn't have starved to death and might have drunk water out of the toilet (which usually automatically refill if they get low enough to lift the lever)
...something strange in that assumption, either about dogs or toilets.
Toilet
bowls (in the various 'western' types of potty-porcelain that you'd expect, at least) don't refill unless you flush (and eventually get below the U-bend level, which then opens up the the usual air-locking from the septic pipes). It's quite a party trick (though not unknown) for a dog to flush a loo. (Ditto for unconventional bidet use; see tap-nudging, below, but also the assumption that the fixtures in this room were not relevent.)
The
cistern autofils (when flushed, or otherwise emptied), but I don't know of many that are (intentionally) left open to drinking water out of. I mean, I regularly have to take the top off one of mine because the valve is a little sticky and the ballcock floats up but doesn't
quite stop the flow (it starts draining down the 'overflow', which - in this particular case - results in a trickle into the bowl, rather than the usual out of the wall). It's only a very slow trickle, but I do like to take the cistern lid off and manually press down on the thing that the levered stopcock arm hasn't quite pressed down enough upon, to stop it entirely, then replace the lid. (I'm not tempted to leave the cistern lid off, with or without dogs in the house.) But I can't believe that this couple (with a couple of occasional maintenance workers on tap,
NPI!) would put up with the same situation as I do, never mind go full slob and leave the top off to save the (minor) effort of removing it after every other flush whenever there's the audio cue is that it's "doing it again...".
Though my best guess was already that the surviving dog left inside (assuming that it wasn't just a dog that happened to be found inside a bit of the house with the external door left open, and - like the dog that was outside - could 'happily' be in relative shelter from the current climate
or outside where puddles form and - just possibly, depending upon the dog - food could be found) just had enough water in the water-bowl (maybe an autodispensing one, and perhaps then even a hopper-fed autodispensing dry dog-food thing as well, 'cos any reasonably wealthy person might well have invested in such a labour-saving gadget to do at least part of the job of caring for their pets) or an indoor fountain (or fish-tank? ...though they frequently have hard covers on as well) or was even one of those that had learned to nudge a tap(/faucet)-lever (if not nudge it back), or
did learn that within a couple of days of desperation.
Again, all this on the initial information that
one dog was (in a closet/cubbyhole?) in the bathroom with the wife, when it'd be not unnatural to assume the bathroom door was closed by habit/spring. And the other was therefore roaming "in (a part of) the rest of the house", presumably not ever there (in the apparently deadly bathroom) at all, to access the loo-water in any form.
Maybe not accessing the area where the husband was laying, either.
But I still haven't tried to update my original information, let alone bring out the camera-friendly "glass whiteboard" and started scrawling floorplans (and, for some reason, mathematical equations) across it, or pinning photos of everyone the couple knew to a basement wall, with loads of red string connecting them and random bits of paper from household bills to half-redacted US Government documents.