You have it correctly in Bankruptcy some assets are protected the protection depends on the state. In particular in Tx your primary residence is protected, and under federal law a 401k is protected. So if you loose a lawsuit above the limits you file for bankruptcy in which some assets are protected. So in that case you really don't need to include those assets in the umbrella limit.
I still don't see this. Let's take several cases with a $2M lawsuit that is covered by your umbrella up to its limit:
1) You have $1M total net worth, none protected, and a
$1M umbrella, and a $2M lawsuit. You are left with nothing. The $1M umbrella did not 'protect' your $1M net worth. They got $2M.
2) You have $1M total net worth, $500K of that is protected,
NO umbrella, and a $2M lawsuit. You are left with the $500K that was protected. They got $500K (and you got no legal assistance).
3) You have $1M total net worth, $500K protected,
$500K umbrella (per your suggestion), and a $2M lawsuit. You are left with the $500K that was protected, same as with no umbrella. The $500K umbrella did not 'protect' your $500K of unprotected net worth. They got $1M.
4 (corrected)) You have $1M total net worth, $500K protected,
$1M umbrella, and a $2M lawsuit. You are left with the $500K that was protected, same as with no umbrella, same as with $500K umbrella. They get $1.5M.
Now a larger umbrella:
5) You have $1M total net worth, $500K protected,
$2M umbrella, and a $2M lawsuit. You are left with the $500K that was protected, same as with no umbrella, plus the $500K of unprotected net worth - the umbrella paid the entire $2M.
What you really want for your umbrella amount is the largest $ amount that someone sues you for (an unknown). But the $ protected in your State are protected regardless of umbrella amount - I see no connection.
-ERD50