An example to make to question more clear: With the use of nuclear power plants come several risk-costs (the risk of a nuclear disaster). These costs aren't included in the energy price and there is nobody who pays for it. So are they considered as external costs?
In the particular case of nuclear power plants, yes, the risk cost can be considered as a negative externality.
That's because nuclear power plant operators are explicitly limited by law in their liability for third-party costs in the event of damages to those third parties. The third-party risk they present could run into trillions (\$/€): at Fukushima, the current cost is estimated at \$200bn and rising. But operators' liability is capped at a much much smaller amount: this differs by country, but typically of the order of a few hundred million to a few billion (\$/€). This means that operators do not have to spend as much money as they otherwise would, on reducing those third-party risks.
If nuclear plant operators had to buy insurance to cover that entire risk, then it's they would be even more uneconomical than they already are. That is, their cost base would be much higher. The direct third-party damages are not paid by the operator, nor by the consumer; but instead are paid by the taxpayers, in the countries that have to clean up after accidents. So, the Japanese taxpayer has borne a large share of the costs, because Fukushima; previously, the USSR did, because Chernobyl - but in that case, some costs were spread all over the Northern hemisphere, due to widespread distribution of the radioactive material; for example, there were restrictions on farming in polluted areas, vast distances from the plant, for decades afterwards.
So, the consequences of the risk are borne as public subsidy. The risk premium itself is not a cost borne directly by anyone: it's an uninsured risk. So, it could be viewed as a negative externality that, if priced in, would move the supply curve.
Note that if you were to refer to these risks, and their consequences, explicitly as subsidies and negative externalities, then you're probably going to have to provide an accompanying explanation (as I've attempted to do above - hopefully you can be more succinct!), as for much of your audience, it won't be immediately obvious as to why you're using those labels.
In the restaurant business, there is always the possibility and a non-zero probability, that a customer gets poisoned by the food.
Businesses implement various measures to guard against such an incident, from simple cleaning routines and raw food inspection, to sophisticated mquality assurance procedures. These measures absorb productive resources and so are reflected as costs. These costs are eventually included in the price-list of the restaurant.
On top of that, restaurants purchase insurance policies that will cover the indemnity costs when such a risk is realized. These insurances policies are production costs also, and they are eventually reflected in the price list of the restaurant.
In the nuclear power plant business, there is always the possibility and a non-zero probability, that some customers, alongside some employees, will get poisoned by radioactive materials, or even be blown to pieces by the initial explosion. Businesses of the sector implement various measures to guard against such an incident... etc.
Since the OP is asking about contingent costs associated with uncertain events, the concept of externalities would not be accurate here, since under these concept we classify realized detrimental consequences of production processes that are not, or are difficult to, be priced (natural resource depletion and air pollution being the archetypal examples here).