Scott, the term is " Mysterious Disappearance " and it is an exclusion found in most if not all homeowners policies. FWIW, most insurance that covers theft requires evidence of forced entry. Too bad about the Schlage deadbolt issue. Back in the day, when insurance actually covered claims, we didn't have to deal with as many exclusions. Over the years, the insurance industry has modified or amended their policies to exclude in one way or another every type of claim other than the basic fire and wind losses. And for those, they have added significant deductibles. But only if you live in an area that is subject to fire and wind losses. So if you live in the desert with nothing to burn, fire insurance can be purchased quite reasonably.
Regarding your personal liability, as Gary Wizard and Sarge point out, it's a challenging area for full timers. Not sure if they're still available, but when I was selling insurance a policy called a Comprehensive Personal Liability could be purchased. It provided coverage for your personal acts not related to the ownership, operation, maintenance or use of an automobile, motorcycle, boat, snowmobile, or similar. Example, you forget to keep your dog leashed. He takes off and bites a neighbor. Not covered by your vehicle insurance. But like an auto policy, it provided coverage for negligence arising out of your acts. Not sure many of todays young insurance underwriters (order takers) ever heard the term. The coverage is automatically included in a Homeowners policy. Renters are also able to purchase a policy which covers their personal property and personal liability.
Regarding an umbrella policy, there are two kinds. One that provides coverage only in excess of your scheduled policies. That's really an Excess Liability policy. A true umbrella policy covers loss in excess of your scheduled policies, (auto, homeowners, boat, etc.,) and, subject to its own exclusions, coverage in excess of a stated deductible, maybe $10,000, if your primary policy doesn't cover the claim. That said, if one of your underlying policies expired and was not renewed at the time of the claim, the deductible will be whatever the required limit of the underlying policy was.