I found an answer here: What is $v \, dp$ work and when do I use it? It says that $V\,dP$ term is isentropic shaft work.
Let us consider an adiabatic piston gas system which has some sand mass on top of the piston. The mass is slowly decreasing such that the process is reversible. So for the gas in the system $PV=nRT$. Now let us differentiate on both sides $PdV+VdP=nRdT$, (Assuming that gas does not dissociate). For adiabatic process $-dU=-nC_v\,dT=\delta W=P\,dV$ so putting $P\,dV$ as $-nC_v\,dT$ we see that $Vdp=nR\,dT+nC_v\,dT$.What does the $V\,dP$ term signify for non flow systems? Are variable external pressure systems even considered closed systems? And if it implies some kind of work, why isn't is considered in $dU=-nC_v\,dT=\delta W=P\,dV$?