They can give their proxies but only after a quorum has been established and the EC members actually present have then agreed to accept proxies.
For instance Chairman turns up with two proxy votes in pocket. Two non-cronies also turn up. Meeting is quorate. Chair then asks members present to accept proxies.
They don’t have to and since there is a clear intent to fill EC positions with “phantom” members to give the Chair all the power to do as he or she pleases, they really shouldn’t. It’s not illegal – just highly immoral and the majority of owners actually at the meeting shouldn’t go along with it.