You should first understand some fundamental principals about push-pull controls so that you can visualize what might be happening inside.
You should consider the outer sheath as merely a guide (or pipe) for the inner core. The sheath is flexable (for most applications) as a convenience for ease of installation only.
This means that, for most throttle,mixture,prop gov. applications, the sheath is not something that moves during normal operations.
The inner core is almost always a flexable wire core. When the core is inside the sheath, its movement is constrained to just slide backward and forward inside the sheath.
There is, also, a small amount of sideways movement possible as the core is somewhat smaller than the ID of the sheath.
What can interfere with this fundamental operation is congealed or cooked out lubrication, or, physical damage such as the sheath being crushed.
This covers what is happening along most of the length of the control.
Problems usually arise at the ends. At the engine end, there is almost always a stud which is attached to the core. This stud slides in and out of a rigid dust tube, which acts as a support.
The purpose of the dust (or support) tube is to limit the motion of the stud to moving in and out from the sheath, while also swinging thru a small arc.
In other words, it keeps the stud in line with the work it has to do.
When the stud is fully pushed outward, it is mostly outside if the dust tube, and, since it is attached to the core, a certain amount of the core is now outside of the sheath and is no longer supported by the sheath.
Since the ID of the dust tube is much greater than the OD of the core, the core now has the freedom to go out of column, and, given enough compression, even assume a cork screw shape, or, open up and become a bird cage like structure.
This is a key to some common failure modes: the core is overloaded, in compression, and becomes permanently deformed, and therefore, unable to be pulled back into the sheath.
Another common failure is that the swivel joint of the dust tube fails, the tube is now free of the sheath and no longer constrains the movement of the stud. The stud now flops around and the core permanently bends.
Of course, there is also the failure from physical damage: the dust tube gets bent, or crushed, and now the stud cannot slide freely inside it. This damage you can readily see.
These same principals also apply to the other end of the control, inside the cockpit. If the control is attached to a quadrant, then the quadrant end will be, in construction, almost identical to the engine end.
There may be differences in the size and/or length of the parts, but the principal is exactly the same. If the control is a panel mount type, then the considerations are:
(1)when the panel tube and knob are fully pulled back, there is going to be unsupported core outside of the sheath, an amount equal to the length of the stroke of the control.
(2)the panel tube will almost always have two locking mechanisms: internal teeth will engage an internal, open spring, which prevents the knob from moving back and forth without pressing the release button, and, there will be some sort of an adjustable packing gland to prevent the panel tube from creeping (rotating) while locked.
Again, a common failure mode is that the unsupported core wire gets damaged when an excessive compressive load is applied, and now the core can no longer re-enter the sheath.
Keep this in mind when tugging or pushing a cranky control. The core is strong enough that you will not break it when tension is applied. The unsupported core will fail if given enough compression load.
This implies that once the core has been damaged in compression. the control is now trashed.

What about a control that is getting stiff?
First, verify that it is the control that is binding and not what it is attached to.
Release the engine end from it's connection and try again.
A control that is getting stiff probably has failed lubricant, and, the residue of overcooked lubricant. This is a situation in which the control can probably be saved.
The control must be removed from the aircraft.
Using tie wraps, coil up the control and place in a suitable container. Pour in enough kerosene to completely immerse the control, and allow to soak for about a week.
While the control is under the kerosene, you should move the pilot end of the control back and forth, which will pump the kerosene into the control and out the engine end. You will probably see a black cloud of crud being pumped out of the engine end. Continue until the fluid pumps clear.

Vernier panel mount only: the control creeps.
In this situation, the packing gland has dried out and shrunk, and/or just worn.
This is usually easily fixed.
The panel tube (inner and outer) must be released from it's mount. The outer panel tube, just behind the knob, will have a large nut that the inner tube slides inside of.
Behind the panel is another nut which actually secures the mounting of the tube. Once this jam nut is backed off to release the panel tube, the outer nut on the face of the panel can be tightened.
First completely loosen this nut and allow it to come loose from the tube. Inside of this nut is a packing gland(s) and maybe a domed washer.
You should try to work some TFE  grease both into the outer panel tube and behind the gland nut. Lubricate the inner tube. Screw the panel nut back onto the outer panel tube and tighten it down.
You will probably be able to adjust the friction level to a serviceable level.

Lubrication:
This may be somewhat hard to do. The result you want is just a trace of high temperature tolerant lubricant inside of the sheath and core.
Do not attempt to pressure pump any sort of grease into the control as it will go into hydraulic lock.
Be very carefull with lubricants in spray cans.
Is it suitable for high temp. service? What about the carrier? Is it a solvent which will attack plastic components?
Many modern push-pull controls have an engineered plastic liner which may be attacked by the carrier in a spray lubricant. Also, since the liner is closed and solid, whatever you may put on the sheath is not going to get inside to the core.
We have heard of people using a pressure pot and hosing to force something very thin (like hydraulic fluid)
into the control from one end. This can very easily go wrong.
The safest thing is the total immersion bath. Mix some 30W engine oil into clean kerosene and soak.
The kerosene will completely evaporate away and leave behind just a trace of oil, which is what is best.
You could also hang the control up and allow the oil to drip in, from one end to the other. This takes a really long time, but is much safer than any sort of pressure rig.



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