or connected any power to the 4051.
This makes no sense. All "chips" have to be powered in the first place to provide useful operationallity. By looking at the internal wiring, one could deduce what will happen without any Vdd applied, but this is more or less a forensic post-mortem...
In the first place, no voltage should be applied to any input pin above Vdd+0.6V or below Vss -0.6V. When a chip is not powered, everything is critical, and - as said - undefined.
An analog switch (4016/4066) or multiplexer (4051/52/53) is not a "relay"!
As an aside. In contrast to the given link, note that the connection is bi-directional, there is neiter input nor output but "throughput" 
The internal resistance is about 100 ohms.