The underlying-limits requirement is a condition of coverage rather than a recommendation, and its failure mode is what makes it worth understanding. An insurer writing an umbrella specifies minimum liability limits that the auto, homeowners, or renters policies underneath it must carry, and those minimums usually sit above what a household already has, so buying an umbrella tends to improve the base policies as a side effect. Umbrella forms name that required coverage as a defined term and then say what happens if it is not maintained, so the consequence of letting an underlying limit slip is written into the policy rather than left to an adjuster. The common treatment is that the umbrella still begins where the required limit would have ended, meaning it starts paying where it always would have started and the household funds the difference between what the reduced policy actually paid and where the umbrella's layer begins. Which treatment applies is a question about the particular form, and the required limits themselves vary by insurer, which is why both are worth confirming each time an underlying policy changes rather than once at purchase.
Which underlying policy a claim arrives through is not something the household chooses. Personal liability is not bought as one thing; it comes attached to each policy, with limits set at different times for different reasons, and the lowest of them is the one a given claim will find. A household with a strong limit on the house and a decade-old default on the cars is exposed through the cars.
The exclusions are where a reader's real risk usually lives. Business and professional activities are generally excluded from a personal umbrella, which matters because a homeowners policy also excludes business liability, so a business run from home can be uninsured on both policies at once and needs business liability insurance to answer for it. Intentional acts are excluded. Liability assumed under a contract is commonly excluded or narrowed. And liability arising out of a vehicle, boat, or recreational vehicle that is not scheduled on an underlying policy is commonly excluded too, which is the trap when a household adds a boat or a young driver and updates only one policy.
The pricing argument is a ratio rather than a number, and the ratio is the part that holds over time. Because claims that large are uncommon, an additional million dollars of liability coverage costs substantially less than the first million of coverage on the underlying policies did, which is what makes an umbrella one of the highest coverage-per-dollar purchases available to most households. Current premiums are quoted by insurer, state, and household, and the figures that circulate come from sellers, so this entry states the shape and not a price.
What an umbrella does not do is worth stating as plainly as what it does. It pays nothing toward the household's own losses, so a reader who buys a million dollars of umbrella coverage and then has a house fire has bought nothing that responds. It is not a substitute for adequate underlying limits, because it sits on them rather than replacing them. And it does not protect income as such; the exposure it answers is a judgment that can reach both accumulated assets and future earnings, which is why the test for whether a household needs one adds those two together rather than looking at net worth alone.