I have paneling on every wall in the house. The landlord does not want the walls to be painted. Is there a way to paper over it without damaging the panel when the wallpaper is removed?

Hi. I'm hoping someone can help me figure out why, shortly after painting my parents' home, large dirty stripes (approximately 1-2 feet in width) show up through their paint? Starts at the top and works down. They had their vents cleaned as they were promised that would help - and it had no effect. What is this all about? How can I avoid it the next time I paint their walls/ceilings. The dirt also shows up through the ceilings. Interesting enough, I had a home in Kentucky for a while that was brand new. And I noticed similar striping showing up after a couple years. It appeared to be between 2x4s. Appreciate any input.