A temporary fix of a couple years
...I gotta write that down...I feel like Auntie Bea...chaulk and cock are things which will not help...one will wake you up at sunrise, the other is good for murals on the driveway.
A good silicone caulk will help temporarily. The good stuff is good for 50 years according to the manufacturer, but you need something to attach it to...the rotting building like guyod said will not do.
My opinion is to contact the owner, then the 411, then move if nothing is done.
Sorry for being nit picky, I'm home with the flu and needed some off humor. Nothing personal, just tryin to have some fun.