The answer is ‘NO”.
The U.S. Geological Survey estimates that landslides cause an average of $3.5 billion a year in damage. https://on.doi.gov/2ASDPCh
Homeowners insurance typically doesn't cover landslides or mudslides. That's because both are considered a form of "earth movement", and like an earthquake or sinkhole, they're generally excluded from a standard homeowners insurance policy.
A Flood policy issued by FEMA (Federal Emergency Management Agency) might cover certain types of mudslides but they must meet certain criteria. See below for the definition:
According to FEMA, a flood is a complete or partial inundation of two or more acres of land, from inland or tidal waters; or from a rapid accumulation of surface waters from any source; or mudflow. So technically, under a National Flood Insurance Program (NFIP) policy, you would likely be covered. http://bit.ly/2D3B06A
So in many cases, the homeowner will have to pay for damages to their home out of their own pocket! Sounds like it could be financially devastating.