When will an insurer investigate for fraud?
Well, not typically on a small claim. However, on major claims they will fact check to start and then if something doesn't feel right, they'll investigate. If a boat catches fire at a dock and is destroyed, they're definitely going to find out if someone was living on it. If a boat mysteriously sinks at sea, they're going to find out where you stood on payments on the boat. They also know the signs of fraudulent action by those in divorce proceedings.
As to personal belongings in a house or on a boat, I'd suggest everyone have an inventory of items and, in today's world where it's so easy, have current photos of every room, every cabin on a boat. While there may be an agreed value on the boat or house (although not on many policies where it's stated but not agreed), there isn't on personal items. It's amazing how the flea market painting is suddenly a Picasso when destroyed. However, most policies on homes require those items and jewelry to be under separate policies as the limits for those items on basic policies is generally low. Just because you have a limit of $100k on contents, doesn't mean that's what they'll pay, and whether you have replacement value or depreciated value is a huge difference. Here is a typical personal effects clause.
“Personal effects” are any items owned by the insured that
do not exceed in value the amount stated on the
declaration sheets or in Section B3(e) below and are
normally worn or carried on a person while on board the
insured vessel(s). Personal effects do not include jewelry,
watches, cell phones, PDA’s, eye wear, furs, fine arts,
collectibles, money, credit, debit or other bankcards,
checks, notes, stocks, bonds, or any other financial
instruments, securities or intangible property.
And back to Pau's point number one. If you own any insurance policy you haven't read, you need to go read it soon. Every word. Every exclusion. Every requirement placed on you.
I've read some pretty tough exclusions on policies from very reputable insurers. Here's one on theft:
Theft is only covered if the items are stolen from locked
premises and there are visible signs of forced entry.
Basically if you don't lock your doors, you're not covered per that.
And one on sails and canvas:
Sails and canvas damaged or lost due solely to
foreseeable wind and weather conditions are not covered.
So, hurricane Matthew destroyed your canvas. Not covered per that.
I've seen people on the lake have boats sink due to muskrats eating through the bellows and find out they had a vermin exclusion.