Thanks for the information I have received.
I have ran a Google search for the word 'foxing', and what I have seen
does indeed confirm it's a fungus that develops in humid conditions.

However, recommended treatments I have encountered are done by experts
and are far more expensive than the worth of the bills I have. Is
there a cleaning product I can buy from the store ?
Regarding the first question, I am using Vinyl or Nylon paper-holder
for A4 paper size. Is it a good solution to remove all the air from
the bag and seal it? Will this stop the decay on damaged bills ?