My parents home partially burned down last summer, and while the contractors and adjusters were at the scene and reasonably polite, it was the gangs of thieves who stopped by after midnight to try to loot the place that really drove home the tragedy. City police maintained a frequent drive-by and advised us to keep someone on-site overnight, until what was left of the house could be secured.
Twice that first night, groups of people in vans pulled into our driveway and approached the still-smoking house, only to run back and screech away when they saw my father or I come around the corner of what was left of the garage. This was one of the few times I wished I had owned a gun – the insult-on-top-of-injury attitude that these wannabe thieves demonstrated really made the ambulance chasers and crooked contractors seem like reasonable fellows.
In the aftermath of a tragedy that leaves significant assets remaining that you cannot protect, make sure you keep people you trust on-site until an experienced contractor can board up and secure the property adequately. Best bet is to find a contractor that offers one to several battery-powered motion-detection lights / cameras that you can rent for a few days, and these are well worth their steep cost. They tend to indicate a contractor that is more concerned about protecting your remaining property, than simply slapping some boards over the doors and calling it a job.