Is it possible to have the speakers on the TV work with the Headphone Jack being used or connected?
Yes it possible however this needs a hardware modification done by a technical person.
Once this modification is done it is permanent, the only way to reverse this function is another hardware modification to return it to the original state.
This cannot be done via software control.
A Solder link needs to be made on the opposite side of the Headphone Jack of the Main PCB – as per the image below.