Leaking sky roof slider, staining interior - 2008 Jeep Liberty

https://www.justanswer.com/jeep/3vqz2-2009-jeep-liberty-sky-slider-option-sky-slider.html

This, Unfortunately, is a very common fault on the Jeep Liberty. There is also problems getting replacement parts for them. This seems like a silly question but have you checked the fuses for the roof? Try this website for the fuse box diagram. Check fuses J22 and M6 in the engine bay fuse box.

https://fuse-box.info/jeep/jeep-liberty-kk-2008-2012-fuses-and-relays
If you remove the inside roof light in there is access to the two motors that power the roof. You can use a 6mm 'Allen' key, (Hex key), to slowly hand crank the motor if it isn't closed properly. There are separate motors for the front and rear sections.
There are specialist companies out there that do body repair work that might replace the whole thing with a fixed position glass roof or even a solid metal roof panel. These solutions will NOT be cheap.

use a solution of bleach and use a spray bottle to spray on the stain
just leave it ( no wiping, rubbing etc ) and in a few days the stain will be gone
there is a product on the market that is advertised to remove stains on ceilings but bleach did mine

check fuses yet?
check for jam or debris?
get it serviceds
read the FSM book? on diagnosis?

You need to remove most of the interior panels that prevent the liner from coming out. Than you have to carefully bend it slightly and go out the back door with it.

its that sun roof leaking and its showing roof water stains or the floor pans may be rusted leaving holes in it or the roof is so rusted that there are holes in it that can not keep water out.

If it has a sun roof, check it for leaks or there are drain tubes coming off of the sunroof that drain water from the roof. If the drain tubes are blocked the water could come inside. If the inside headliner has stains on it, they may be water stains which tells of a leak.

It is going to be the seal in your moon roof. Unless you have holes in the top of your car you can be sure that the water is coming from there.

Why don't you see if you can find a used one at an auto wrecker.

Never need a dealer for any auto repairs ,why do you think ,there are 200,000 repair shops on every corner?

The roof drain hose may have come off
Loosen headliner and check out