It would be very difficult in today's Western suburban world to survive a scenario like this.
Some cultures which survive at a subsistence level even today might slip through the radar.
A few might be able to hide with sympathetic non-Christians who would feed them (however their buying patterns would give rise to suspicion that they were covering for someone eg. buying extra food, clothing etc.).
For example someone called Jack might be sheltering an asthmatic Christian friend but the computerised system would pick up that -
"5th June 2019 - 9.13 am Subject purchased asthma puffer from Browns Chemist.
6th June 2019 - 7.30pm Subject purchased four TV meals from late night store before going home.
Analysis - subject's buying patterns suggest he is buying more food than he needs. Subject is not known to have asthma or other allergies.
Recommendation - subject's home to be monitored."
I've got a booklet at home published by the "Commission for the Future" which was set up by the Australian Hawke government way back in the 1980's. They published a number of booklets, but this is the only one I've got. It's subtitled "Towards a Cashless Future", and it was chaired by Philip Adams, who is an Australian atheist, albeit with his heart in the right place in most ways. So it's hardly a religious publication.
At one point an example like the above was given, but in more detail. They also pointed out that as far back as 1975 a think tank of American lawyers opined that the easiest way for a government to keep a close eye on it's citizens would be electronic commerce, or if you like, a cashless society. They'd know what you buy, when you bought it, where you bought it, and whether it was consistent with your normal individual buying patterns.
I'm probably an oddity as a Catholic who believes there's something in the "Mark of the Beast", even though the technology already exists for it to take place. The only thing lacking at the moment is an appropriate political trigger eg. a very powerful terrorist attack, or a nuclear war, or some other crisis.
I don't believe in the Rapture, and those of us who might have to suffer through the rule of the "anti-Christ" will have to do just that. There won't be any magic carpet from heaven reaching down and just pulling us out because it's difficult. God didn't pull out the believers from the Black Death, the Mongol hordes, the Vikings, or two World Wars, and He won't pull us out of this one either.
The warning isn't there for nothing. There's a hint in the Catholic Catechism of this "final trial" -
The Church's ultimate trial
675 Before Christ's second coming the Church must pass through a final trial that will shake the faith of many believers.574 The persecution that accompanies her pilgrimage on earth575 will unveil the "mystery of iniquity" in the form of a religious deception offering men an apparent solution to their problems at the price of apostasy from the truth. The supreme religious deception is that of the Antichrist, a pseudo-messianism by which man glorifies himself in place of God and of his Messiah come in the flesh.576
676 The Antichrist's deception already begins to take shape in the world every time the claim is made to realize within history that messianic hope which can only be realized beyond history through the eschatological judgment. The Church has rejected even modified forms of this falsification of the kingdom to come under the name of millenarianism,577 especially the "intrinsically perverse" political form of a secular messianism.578
677 The Church will enter the glory of the kingdom only through this final Passover, when she will follow her Lord in his death and Resurrection.579 The kingdom will be fulfilled, then, not by a historic triumph of the Church through a progressive ascendancy, but only by God's victory over the final unleashing of evil, which will cause his Bride to come down from heaven.580 God's triumph over the revolt of evil will take the form of the Last Judgment after the final cosmic upheaval of this passing world.581