There are certain APs with PoE passthrough, and they will offer it while themselves PoE powered if they are on 802.3at. However, this is pretty much limited to the wallplate offerings as the PoE out is designed for IP phones.
I'm fairly certain that the above will have difficulties with standard Ethernet. For one, the added interference from double the PoE is going to cause some headaches, and the 2nd AP would have to mesh for any real chance. If you do this, I would suggest only terminating the PoE pairs of the second AP as having it attempt to use the Ethernet will only result in collisions and more frustration.
How long is the cable run in question?