This may simply be your headlamp delay off feature in operation!
From memory: you must turn the headlamps OFF before turning the ignition switch to off.
If you turn the ignition switch to off before turning the headlamps off, the headlamps will remain on for whatever period of time you have them set to remain on.
From the Jeep Liberty's owner manual: wrote:
Customer Programmable Features
Press the MENU button until one of the display choices
following appears:
Headlamp Delay
When this feature is selected the driver can choose, when
exiting the vehicle, to have the headlamps remain on for
30, 60, or 90 seconds, or not remain on. Pressing the STEP
button when in this display will select 30, 60, 90, or OFF
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Supporting Vendor and Moderator of LOST05 Jeep Liberty CRD Limited
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