That's not to say that the theatrical Die Hard 'rip-offs' were cheap, as obviously the likes of Air Force One or Under Siege are very expensive pictures. But if you're a small-time film studio, you now have the perfect formula for cheap action. Just take a single location, as stripped-down or as elaborate as you can afford. Maybe it's a glitzy hotel or maybe it's an underground science lab where every room is basically the same room. Just take a single action hero who is stuck by himself (or very rarely herself) to fend off the bad guys. Add a dozen or so hostages of varying types and attractiveness. And *presto*, you've got an action movie. How elaborate to make the fight scenes, how prevalent to make the squib work, how numerous to make whatever explosions you can afford, that's all up to you and your budget. If you have extra money to burn, hire a somewhat notable actor as the lead villain and/or add a secondary doomsday scenario that introduces a ticking clock. This helps as it allows you to maximize violence by basically killing all of your hostages (except the hero's love interest or family member of course) while still allowing the hero to save the day.
If you had HBO and/or Showtime back in the late 1990s, you've probably sampled a bunch of these. You've seen the high end entries like "Die Hard at a beauty pageant" No Contest (with Sharon Tweed as a rare heroine, Robert Davi as the supportive cop, and Andrew Dice Clay as the heavy) which has enough production values and special effects that I'm surprised in hindsight that it didn't go to theaters. The film contains a ridiculous amount of blood (a single bullet unleashes a paint can's worth of blood), a sky-high body count, plus several honest-to-goodness explosions. Then you've got stuff like Memorial Day with Jeff Speakman, who along with Jeff Fahey, did a handful of these back in the VHS twilight era (think Hijack with Ernie Hudson). Speaking of sky-high body count, the films often compensated for their lack of production values with rather wanton violence that would make most studio action films recoil in horror. Chain of Command ends with the hero failing to save the president (Roy Scheider) and failing to stop the terrorists from nuking a chunk of America. Icebreaker (Die Hard at a ski resort) spent its money on Bruce Campbell as the villain, although one hopes that hero Sean Astin merited more than scale in his pre-Lord of the Rings days.
There are dozens (hundreds?) of other examples I could rattle off, but the sheer number is the point. In the pre-digital age of direct-to-VHS, a large majority of action pictures were low-budget Die Hard rip-offs precisely because the Die Hard formula could be redone on a shoe-string budget. Albert Pyun's Blast (Die Hard with a kidnapped Olympic swim team with Rutgar Hauer and a very young Shannon Elizabeth as one of the hostages) cost $700,000 and looks even cheaper. The film has almost no special effects work and a climactic explosion that is literally animated like in a Road Runner cartoon. A single location, a handful of hostages to be menaced and/or executed, a handful of faceless enemy occupiers, a single regular guy hero (usually a security guard or disgraced former cop) who has something at stake because one of those hostages is his girlfriend/wife/ex-wife/secret crush. If you have the money, hire a Bruce Campbell or Andrew McCarthy (The Heist, or Die Hard in a single room of a call center) to be the villain. Daniel Baldwin was being ambitious in 2002 when he directed and starred in Tunnel (one of many many "Die Hard on a train"s) while casting Kim Coates as the villain.
Many if not most of these films have been (justifiably?) forgotten. But they are in some ways Die Hard's most endearingly weird legacy. By following the blue print, every action actor could have their own Die Hard and the next Die Hard could come from anywhere. So when others scoff that Lock Out had cheesy special effects or that Olympus Has Fallen (seeing it tonight) has occasionally cheap-looking FX, I can only smile. Maybe they aren't odes to Die Hard but to the countless Die Hard rip-offs that lined the walls of Hollywood Video waiting to accidentally rented on a late-90's/early 2000's Saturday night. I can hope that Olympus Has Fallen is as much ridiculously violent and dumb fun as No Contest.