Think of a self-insured retention as the umbrella's own deductible. It comes into play when the umbrella covers a claim that no underlying policy covers. With no underlying limit to sit on, the umbrella drops down and the insured keeps a stated first slice of the loss.
How it is applied: the insured pays the retention, and the umbrella pays the rest of the covered loss up to its limit. Example: an umbrella with a $1,000 SIR covers a $25,000 claim that none of the underlying policies cover. The insured pays $1,000 and the umbrella pays $24,000.
When an underlying policy does cover the claim, the underlying limit does the job a retention would do, so no SIR is taken. Example: a $300,000 auto liability limit and a covered $350,000 auto judgment. The auto policy pays $300,000 and the umbrella pays $50,000, with no retention.
An SIR is not the deductible on an underlying policy. It belongs to the umbrella, and its amount is stated in the umbrella's declarations.