Mostly Nope.
Largely due to how % armor penetration stacks with itself. If you have 50% and 50% armor penetration, you will penetrate 75% of a target's armor.
Because you penetrate 50% of it, then penetrate the remaining 50% by 50%.
Due to this interaction - the only way to get more than 100% armor penetration is if you have 1 source of armor penetration that gives more than 100% armor penetration.
At least with % penetrations alone.
With both %armor pen and flat armor penetrations, they are physically incapable of reducing the effective armor of an opponent below 0 because of the game's codding, so even with a really crazy combo you can't reduce armor any lower than 0.
All that said - flat armor reductions are quite capable of reducing armor below 0, But they are applied before any armor penetrations come into play, so you need to reduce over 100% of an opponent's armor with such flat debuffs alone.
Due to how % stacks with % as mentioned above, %armor reduction debuffs don't really help.
With where base armor and per-level armor on champions is, as well as a complete lack of itemizing for flat armor reduction, it's pretttttty much impossible to reduce armor below against champions as you'd need a very specific team comp to pull it off.
The squishies squish still manages a solid 60 armor through bases @18, and 75 is much more common for pretty much everyone. Base starts pretty close to 30 by the time you actually do trade with an opponent as well - which is a pretty high number all things considered.
All that said - the low armor on minions/monsters does allow champions with high in-built flat reductions the capacity to reduce minions/monsters well below 0 for some pretty epic hits.
Particularly useful for winning the "largest critical strike" field in the post-game screen. Nasus has the largest flat reduction I'm aware of, his Spirit Fire reduces armor and MR by 40. Manage to get that Triforce's 15% crit chance to kick in on a Q vs. some poor minion, and you can probably get upwards of a 2k crit within a respectable ~33 minute game for ultimate bragging rights.