The US deposit protection scheme does run like that, where there is a defined fund to pay out, and the possibility of exhausting it.
Other countries, such as the UK, do not have a limited fund. All deposits are guaranteed up to the insured limit.
You can say you have an unlimited fund, but actually paying out on it in the instance of a worst-case catastrophe may not always be possible.
Or if it is possible to cover them, it may be due to printing currency and the value of the currency they pay you in may be 10% of the pre-bailout value.