What happens if PD tries to consume more than allowed PSE power provided?
If the Powered Device (PD) draws more power than its class, then the current limit would be hit on the (or other PSE controller) TPS2372 and it would revert to an idle state:


Source: http://www.ti.com/lit/ds/symlink/tps2372.pdf

This should never happen however, as part of the spec the PD needs to make sure that it never draws more power than it's class.