Hi I have 2011 Hyundai i10 1.2 gls. I was driving and the car just stalled. After some fault finding, I determined the pump is fine if you power it directly and the car runs but with the relay it only has 6V (exactly) over the switching poles which are not enough to energize the relay (I tested).
What could be the problem why is it only 6V and not 12V. If I supply power to the pole from the relay to the pump the pump runs so the wire to the pump seems fine. Thanx

 

So, control side has only 6 volts?
And load side has 12 volts?
Or are both sides at 6 volts?

Doesn't matter
You already know what is wrong
Now it is matter of following the wiring to see what is causing this condition
Whether it is corrosion or short or another relay or switch.

 

If I put 12V on the supply side of the relay to the fuel pump it works fine. If I measure the voltage over the switching pins of the relay it measures 6V which is not enough the activate the relay.(I tested). Can it be that the ECU is faulty?

 

Without a wiring diagram to determine exactly if the ECU provides the power or the ground , you are flying a little blind.
What you can do without a diagram is to physically trace the wire coming from the ECU and confirm if it is different at the ECU from what you read at the relay..
Sometimes a poor connection at the fuel pump fuse can get into the picture.