Hi @Elliott D.,
There is a little grey are in your questions that suggest the lender could possibly get involved but it's very unlikely. The only time I've seen that happen is in the case where the homeowner has vacated the property and the bank has foreclosed. (Usually this is a claim in response the place being gutted while vacant)
In most cases it wouldn't be worth it because the insurance company doesn't insure the loan value. For us in California's we see a lot of Million Dollar homes insured for $500,000 (many times much less). That's because $500,000 of the value is in the location and $500,000 is in the value of the physical property.
If your property is in Huntington Beach, and you don't have a ton of equity, I'd wager your property isn't insured for anything close the the loan value. You can always ask your agent for the Dwelling amount or look at your policy declaration page to see what the property is actually insured for.
As reference, there are a couple ways insurance companies will insure your property.
Replacement Cost (RC)- RC is the cost to replace the property on the same premises. You can view this as the cost of ground up construction on the home which may be higher or lower than the loan value.
Actual Cash Value (ACV) - ACV is the cost to replace the property minus depreciation. (RC - Depreciation = ACV) If you have 10 year old cabinets your going to get the value of those cabinets minus 10 years of depreciation.
Agreed Value (AV) - AV is an endorsement you can get through some carriers that states the insurance company agrees to pay a certain dollar amount in the event of a loss regardless of the replacement cost.
I hope that helps you understand your insurance a little better.