I was using this adapter to power a 12VDC LED strip and felt electric shock from the output wire. When I measured the output with a multimeter, I found both 12VDC and 26VAC on it's output. What could be the cause and can it be fixed?
From the photos, this is a very simple inverter power supply. The transformer outputs some 9VAC at a multi-kHz frequency, which is then rectified through the two diodes on the bottom left of the first photo, then filtered through the caps on the bottom.
Because the frequency of the transformer output is in the kHz range, the ripple also is. Your multimeter cannot handle this. The AC reading has no meaning.
I believe its because there is a class Y capacitor between the input and the output of the transformer, to filter high frequency noise (Example). If you measure with a high Z multimeter, you will measure some amount of mains voltage.