Following is a classic example of the difference between the verbs come and go. To complete the gap, should I use coming or going?
Immigration is the process of......to live in a foreign country.
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One meaning of "go" is "to leave a place; depart" and therefore it fits emigration quite well. Another meaning of "go" is "move or proceed, especially to or from something", and so it's possible to use "go" for immigration also, because it refers to generic movement.
You might imagine that "come" is the opposite of "go" and so it should fit "immigration". Indeed, "immigration" and "coming to a new country" are closely aligned.
The problem is that your example sentence seems to be spoken by an omniscient narrator who doesn't reside anywhere. The same voice might say
Spain is on the Iberian Peninsula.
Where is the speaker? Probably not in Spain.
Now, if someone said
He is coming to Spain.
It means they are already in Spain, so it's okay. But in your example sentence, the narrator is not already in the so-called "foreign country".
wiktionary has five definitions to consider:
To move towards the speaker
No. Where is the speaker?
To move towards the listener
No. This sentence doesn't seem to be addressed to a personal listener.
To move towards the object that is the focus of the sentence
Maybe. The difficulty is that "a foreign country" is not a clear focus of the sentence. Which country is it?
(in subordinate clauses and gerunds) To move towards the agent or subject of the main clause.
No. Who is the agent or subject here?
To move towards an unstated agent.
No. Who is the agent?
You could solve the problem by swapping "a foreign country" with a specific country and thereby allowing the listener to imagine the narrator is residing in that country.
Immigration is the process of coming to live (permanently) in the UK.