How does one determine who gets fired after the mass exodus?
Nothing will happen. Wait for the 2030 census and January 3rd 2033.
Representatives are only recalculated after each census. The last census and recalculation was 2020. So no ordinary recalculation will happen till 2030. It's unclear if there could be an extra census, which then might lead to redistricting - the only rules (in the constitution) I can find are, that a census has to happen every 10 years. Current laws are, that it happens every 10 years.
It's up to politics to introduce laws to allow an extra census, but to make it that obvious that it is needed, there needs to be an exodus/death toll of the scale of the black death in Europe (one in 4 dies/moves) or a total depopulation of an area like New York City. Which has 8 million inhabitants, something like 10 districts, and is growing.
Back in 1918 H1N1 killed between 2% and 10% of those that got it and in total about 675,000 (of 103.2 million) in the US, mainly in cities that did lag in their reaction to the fall/winter wave in 1918. As three (not fully) random examples: Philadelphia lost 16000 for something around 941 deaths per 100,000 inhabitants (the town had about 1.7 million inhabitants at the time), LA had a death toll of only 494 per 100,000, all of Nebraska lost between 2800 and 7500 people on a population of 1.3 million - for - for between 200 and 580 deaths per 100,000. Yet despite this very disparate impact it barely impacted the 1920 census.
Not even the hurricane Katrina, which pretty much wiped out New Orleans, did not result in an extra census and restructuring - so it is very unlikely to happen.
2 USC §2b dictates each state gets at least one:
Each State shall be entitled, in the Seventy-eighth and in each Congress thereafter until the taking effect of a reapportionment under a subsequent statute or section 2a of this title, to the number of Representatives shown in the statement transmitted to the Congress on January 8, 1941, based upon the method known as the method of equal proportions, no State to receive less than one Member.
2 USC §2c dictates how many representative districts exist and how many representatives it will have:
In each State entitled in the Ninety-first Congress  or in any subsequent Congress thereafter to more than one Representative under an apportionment made pursuant to the provisions of section 2a(a) of this title, there shall be established by law a number of districts equal to the number of Representatives to which such State is so entitled, and Representatives shall be elected only from districts so established, no district to elect more than one Representative (except that a State which is entitled to more than one Representative and which has in all previous elections elected its Representatives at Large may elect its Representatives at Large to the Ninety-first Congress).
So, one representative per district. One district per representative. District borders are to be redrawn based on the decennial census as demanded in Art. 1 §2 - where it is called Enumeration:
The actual Enumeration shall be made within three Years after the first Meeting of the Congress of the United States, and within every subsequent Term of ten Years, in such Manner as they shall by Law direct. The Number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at Least one Representative; [provisional numbers]
When will redistricting take effect?
Redistricting lags one term behind, and it will not fire or remove a representative from office, whose district is scheduled to vanish - or elect new people. That's because redistricting on the state level can only happen after the reapportionment of the seats has been handed out by the clerk of the House of representatives. Reapportionment has a deadline of 25th January the year after the census. That's after the house term starts. Since at that moment the districts are still in existence, the term of the current holder first needs to run out before the new districts take effect. So the district ceases to exist the same day they leave office on January 3rd.
A good example would be New York:
The 45th district was redistricted from the 43rd District and elected first for in 1944, and was redistricted back into the 43rd District after the 1950 census. It was last voted for in 1950, well before the results of the census were handed out and redistricting happened. So the district ceased to be the same day Daniel A. Reed left the office on January 3rd of 1953.
The 28th Congressional District was established in 1823 and eliminated on January 3rd 2013 as a result of the 2010 census. The last election for its seat was - obviously - in 2010.
As a result, any changes to the district map stemming from the 2020 census will take effect only on January 3rd 2023, and a massive depopulation showing in the 2030 census will have an effect only in the elections for the house that begins its term on January 3rd 2033.
We have a recent real-life example of this sort of scenario. Hurricane Katrina caused massive depopulation of Louisiana's 2nd Congressional District. At the time, this district was mostly the City of New Orleans, as well as a small portion of Jefferson Parish. (The City of New Orleans is a consolidated city-parish, and so is referred to as Orleans Parish in some contexts.)
Orleans and Jefferson Parishes lost approximately 300,000 people in the aftermath of Hurricane Katrina, which was a substantial fraction of the population of the LA-2 district. (My estimate from available data is that it was somewhere between 30–45% of the population.) Despite this, the LA-2 district continued to exist in the same form until Congressional redistricting took place, as scheduled, after the 2010 census. At that time, Louisiana lost one seat and the district boundaries were substantially redrawn. The Representative for LA-2, William J. Jefferson, was not "fired" before this redistricting due to the depopulation of his district (though perhaps he should have been, for other reasons.)
How does one determine who gets "fired"?
By holding an election. Redistricting always affects the next congress, not the current one, and the entire house of representatives is up for reelection every two years. After a reduction in representation, at least two incumbents will be in the same district. If they both seek to be reelected, they will face each other in the primary (if they belong to the same party) or the general election (if they belong to different parties).