A country with land

What would happen if a country is completely destroyed (in the sense of 100% of the land mass being uninhabitable) but most of the population survives? Let's take for example Monaco (not that I would want such trouble on it, it's a lovely place) and imagine that something destroyed all of its land but did it slowly enough for the people to get out. What would happen? Would other countries (and which ones) offer a refuge for its population? Would some country donate land for the establishment of the new Monaco? (I suppose in a generic case the answer is probably not, but in the case of Monaco you really don't need an awful lot of land.) If no land were forthcoming, would the country survive as some kind of entity (for example having a goverment-in-exile that mostly concerns itself with cultural things and a population that is assimilating into the host countries but maintaining some of its old identity)?

What would happen if nobody wanted to accept the population? What would happen if it were a small EU country, for example Luxembourg? Would other EU countries accept its population without much noise or would they start claiming that since the country does not exist anymore it is not a EU member and therefore its citizens do not get to move freely within the EU? What if it were a much bigger EU country?