An independence referendum can be indisputably valid if it is conducted with the co-operation and consent of the sovereign government, and consistently with the constitution of the country.
Examples of this are the Scottish Independence referendum: The UK government consented to the referendum (and passed a bill to that effect) and so it was conducted within the constitutional arrangement of the UK. (The actual result was for Scotland to remain in the UK)
There was the Czechoslovakia referendum, conducted over both nations, which voted for a split into Czechia and Slovakia. Again it was done within the constitutional arrangements of Czechoslovakia.
There was the referendum to leave the European Union - an "independence" of sorts. The constitution of the EU allows countries to leave, following to a certain procedure.
In the case of the Scottish referendum it has been argued that the UK government allowed it because they thought they would win (rightly as it turned out). It has established a principle that the constituent nations of the UK are united by consent. This principle was already in the Good Friday Agreement, which provides that Northern Ireland remains part of the UK while a majority of the people there want to remain, and the UK will not prevent the North of Ireland leaving, if it so desires.
Each country has its own constitutional arrangements. Although the notion of a union by consent is well established in the UK, this is not the case in many other countries. For example, there is no mechanism for a state to leave the USA, so the United States are united by force, regardless of the consent of the citizens. Other countries may have similar arrangements, that prevent a region from leaving the nation unconstitutional, and so making even the holding of a referendum illegal.
In your particular example of refugees would depend on the country: There is nothing in the US constitution to allow it, so such a referendum would be unconstitutional. In the UK it would require an Act of Parliament to authorise such a referendum and legitimise it. Without such an act the referendum would carry no authority. The closest thing I can think of in historical terms to a group of refugees being granted a country is the establishment of "Indian Territory" by the US government in the 19th century, as a place for Indians displaced (or "ethnically cleansed") by the expanding USA.