If you want to have a state which relies exclusievely/mostly on import for food, you have to consider how that state came to exist at all. Let's review a few points that are worth considering.
History
You have to consider how come a state that is strongly dependent on trade for basic resources like food came into existence and, maybe more importantly, kept independent, at least to the point of the story. Different reasons can be seen to explain that. In particular,
- it is a vassal country. It is independent in name only. In reality, it could be seen as an autonomous state within a larger one. The city-states of the Holy Roman Empire could be a good illustration.
- it is a new country. A gold mine was discovered and the first inhabitants are fully dedicated to the new trade and have basically no time for farming. Furthermore, the commerce flourishes and they can import a sizeable portion of the consumed food. But as the time grows, farming around the mines will be done to feed the population and increase the benefits.
- it is a trade hub. It is very well situated on the roads of the international exchange of goods, and as the business got strong, they can actually buy the products transiting through it. I'll come back to those later.
Environment
Unless the state is limited to a city (and even then), some ways of producing food always existed. Consider the following cases.
- It's a small island? For sure there are some fishes around.
- It's in the middle of the mountains? Goats, sheeps, or cows could graze on the mountains sides.
- It's in the middle of a large desert, then the Oasis will allow to get some fruits, vegetables, and feed a few goats for the milk and some meat. Or you might travel around with small herds to get to the best grass plains (Mongolia).
Without any other factors, those lands would harbor only a few people living there. Import is expensive, and you need to pay for it. How, if you have only few resources.
And you also need a reason to import: your population is larger than what the land can sustain.
So generally, you never get to 100% imported food, for the simple reason that you can always produce something locally. And it is cheaper.
Diet
Consider a state which has some small resources. Then, for some historical, economic, political reasons the population start to grow. The state develop strongly its trade capacities. People get richer, and more people migrate to it, and those living there have more healthy children. Slowly the food resources of the country would not suffice for the increasing population. As trade is a major point of the (now, relatively rich) state, they import it. Anyway a lot of food already transit through the state, it is pretty simple to actually buy it.
As some other pointed out, the problem is that to be able to import, you need that other countries are willing to export. That either mean, very expensive or that the other countries have a surplus. Salted-Meat could be transported of ships for some months (think about transatlantic trade, or whaling), but the population of the 17th Century had often a meat-free diet.
the poor [...] subsisted on food like bread, cheese and onions. Ordinary people also ate pottage each day. This was a kind of stew. It was made by boiling grain in water to make a kind of porridge. You added vegetables and (if you could afford it) pieces of meat or fish.
-- [Source]
As other answers state it, the grains could travel for quite some time, to make it a reasonable imported good.
Illustrating examples
History provides a few examples of trade centers with a high importation system. In a few minutes search on the web, I couldn't find any precise values, but you might consider the following illustrations
Venice. It was already mentioned in another answer, but Venice started relatively small and grew to be a major trade centre. It is worth noting that in the 6th Century,
Fishing is the means of livelihood, salt the industry
-- [source]
As they became richer, Venice acquired more land. So probably the net import from other countries wasn't so high. But imports from mainland, or Dalmatian territories was probably high to feed the 170,000 inhabitants of Venice.
Kingdom of Jerusalem. Was a Kingdom built by the conquest from the Crusades. It was established in the 11th Century and ruled by Europeans. The agriculture of the land was quite limited, and they relied heavily on imports. It was a very important trade cross-road, but they nevertheless depended on financial support from Europe. As a consequence,
the kingdom was not wealthy, depending on trade with the Muslims, banking activities, and taxes on pilgrims to keep the government operating and to provide for defense. Though there were some fertile districts, much was barren, and in bad years grain had to be imported from Syria to feed the Christians.
-- [source]
Which probably explain why it was relatively short-lived.
First colonies on the American Continent. They were not self-sufficient, and the imports were very hazardous (time and risks). That explains why the first colonies, and in particular in North America were struggling. When they develop their self-subsistance, they fared progressively better.
Conclusions
I am not very original, but I would conclude like most of the others. It would be hard to quantify the amount of food import that a country might tolerate. But I hope I managed to give you an idea of the several factors you would need to consider when building your state. And on the top of the transportation risk, you add political risk of dependence. And that is often avoided (if possible) by any state.
