I'm trying to rig my character and I don't know how to prevent disconnection between 2 objects when in Pose mode. The problem is shown in the image below. How do I make the foot stick to the joint (ball) no matter where I move the IK?
For non-stretchy leg you should duplicate the foot bone and lets name it Target. The target bone has no parent and is the target of IK constraint. The foot bone is connected to the leg and copies the rotation of target bone with constraint.
Here is how it should look:
I think you dont need the heel bone but if you do you can leave it parented to the Foot bone. Its also good to uncheck Deform for Target bone since it will only control the ik and not deform anything.
For the stretchy-leg set stretch of Leg and chains bones to 1:
But you will not end up with a much pleasing result, the stretchy rig is much more complicated.
If you need to implement also reverse-foot rig or you want to have more advanced stretchy leg you can ask a question specific to that or try the rigify addon, it will do all the work for you.
You'll probably need to set the parent of the bones, and make sure the Connected option is checked in the bone properties panel.
See rigify for extensive examples of this. It uses an elaborate "Stretch To" constraint system. You can use this constraint on your IK bone to achieve what you want.