Yes it is possible, if you have the correct coax.
However you will probably adapters at both ends to convert the coax network line to your network. These can be expensive.
Google 10BASE2 and 10BASE-T Ethernet networks.
I too agree with you as this is possible, as you will find coax to ethernet home networking kit, which comes with coax/ethernet switch and two coax/ethernet adapters that reverse back data and signals on the cable at 800MHz, it tranfers file without disrupting the cable TV signal.