After seeing two houses that have been infested with them, I am POSITIVE you'll never get rid of them without chemicals. The carcasses will never leave. Here is what I base this on:
1) Hunting shack. Old farm house, log walls, etc. Leaks like a sieve. We were replacing some panelling and literally every void not filled with something else was full of these things, mostly dead. Man did that shit stink.
2) Brothers house. Built in the last three years, very tight, new seals everywhere. He's had a terrible problem with them, to the point they only use a garage door to come into and out of the house, everything else is taped shut with masking take. We were up in his attic adding an amplifier to his antenna, and the insulation up there is full of those things. I gotta think his walls are probably packed too. Short of killing all of them in one fell swoop, I don't see how he's gonna get rid of them.
Thankfully my house has been spared. I have seen a few (think a couple dozen, not thousands) this year, which were all promptly removed. I get boxelder bugs, but they haven't been that bad the last few years, and they only last a few weeks.