Can cards that lower rez, play, or install cost (Modded, Amazon Industrial Zone, Monolith, etc.) be used on cards with a lower cost than the cost-lowering card can decrease the cost of card you are trying to lower it by? Here are a few examples:

Can a Modded (lowers install cost of programs/hardware by 3) be used on a Corroder or Cyberfeeder (install cost of 2)?

Can Eureka (lowers install cost of cards by 10) be used on Toolbox (install cost 9), Gordian Blade (install cost 4), etc.?

Can Amazon Industrial Zone (reduce rez cost of ice by 3) be used on a Chum (rez cost 1)?

If so, does the cost of the card just reduce to zero?

Yes.

Unless the card granting the install action explicitly states otherwise, I would say it can be used.

Typically when costs are lowered in this manner, the minimum the rez cost can be is zero (negative costs are not really a cost if it were to give you back credits for playing the card).