Pond fish will only live for a short time if there is no pump running in a pond.
A pump has two functions, it pumps water to your filter and oxygenates the pond water.
If you are thinking of building a pond for fish without a pump, dont do it, it’s not fair to put healthy fish into an environment that is only going to get toxic, make them ill and eventually kill them.
If you have a pump failure or are worried about a pump failure, a lot depends on the time of year, how much oxygen is in the water at time of failure and how many fish you have.
If it’s the winter your fish will live longer, at this time of year your fish are in hibernation and are not relying on plenty of oxygen, they won’t be producing waste so the water quality will not deteriorate too quickly.
If it’s in the middle of summer you will have a big problem, the fish are more active and require a lot more oxygen, they also produce a lot of waste which will turn the water toxic if there isn’t a pump is running to feed the filter, in some cases you could see fish die within 24 hours.
Your fish depends on clean water and oxygen to survive, a filter is used to clean the water and remove the waste (fish poo) from your pond, the filter needs the pump to pump the dirty water from your pond through the filter so it can clean it, without a pump your filter will not be able to do it’s job of removing waste and harmful toxins from the water.
Inside a filter there are good bacteria to clean the water, the bacteria needs oxygen to survive, without the flow of oxygenated water from the pump the bacteria will eventually die, when a new pump is eventually fitted the good bacteria will need time to build up again, so keep an eye on the water quality for a couple of weeks.
You also need the pump to keep the level of dissolved oxygen at a suitable level in the pond water, this is done through the flow of water.
As you can see the pump is the heart of your pond, without a pump your pond fish will not survive.
If your pump fails you need to get a new one as soon as possible, in the meantime check the water quality and do plenty of water changes to keep the ammonia levels low.
If you have an air pump this will supply oxygen to the water but will not clean the water, it’s always a good idea to have an air pump in your pond.