As it turns out, Drexel killed Elivalor family.... the royal family and paid for it in the end. When Elias Drexel offered his life, Eli took it literally and removed his head.
It is detailed here -Session 17 - Eli's Revenge
It's a rumor, and I believe we heard it from Ophelia Reed but, Elias Drexel isn't the man people think he is. Just from personal contact he refused to send anyone out to help Petra Lang leaving the Doom Slingers to rescue her. And when she returned he was strange and distant.