What does it mean "in their computer" is that yes, Imm. got few server racks at CAT building at Bangrak running Oracle databases. And it was set more than 20 years ago. Yes, everything you can see on your passport (related to Thailand) is there. Photos and fingerprints too.
But, very huge but: that much of data called BIg Data, and even running simple update query is a tedious task, but so far it works just fine.
To conclude: it won't be difficult to get a list of (say) all overstayers from Kiwi-land older than 65 with overstay more than 105 days.
Print it and than what? Publish it on some bounty website? Give it as booklet (quite big too) to every policeman? Hang them at 7/11, bus terminals, tube's entrances?
PS: But the bounty idea looks appealing - there're so many farangs willing to do exactly this kind of "volunteering job" )