Dogs can't die of starvation (but they continue to bark of hunger), as far as I understand (I haven't actually tested it out myself).
As mentioned, hungry dogs eat available food (smoked/dried meat that recently finished their processing, for instance), although they can easily reject food in the morning only to bark of hunger throughout most of the afternoon (while you're locked up in a lengthy task, e.g. hide processing) before finally stumbling on the bone pile to start eating from it (and barking a lot while eating). Dogs seem to have a very poor capability of seeking out available food, and seem to rely on their random paths carrying them over the food (their inability to smell nearby predators outside of their cone of vision indicates they don't actually have any sense of smell).
Also, as mentioned, leaving the site seems to put it in stasis: I've had characters away on fairly lengthy trips during the summer and returned to find raw meat still being fresh when it should have spoiled twice over.