They do, and they also need to take responsibility for those mistakes.
While I feel for the OPs relatives, it's their mistake and unless they had specific "Insurance against leaving a running car unattended because I'm a bit of a scatterbrain like that" insurance, it's not Allianz's job to pick up the tab.
There are lots of exclusions in PDSs and people need to get familiar with them to ensure they know where they stand.
It's sounds like the OPs relatives are taking the right approach, this really is just an expensive, live and learn, take responsibility for your cock up and move on situation.