I had a look at some old passports, and I found one where Japan (and a few other countries) placed the stamp on the last few pages listed as "Endorsements", which aren't supposed to hold visas or entry stamps. This wasn't out of necessity; I suspect that the agent opened the passport and this was the first blank page he saw. In fairness, that version of the US passport didn't really differentiate this page from visa pages as much as previous ones did. I did once get criticized in Switzerland because my (also Swiss) entry stamp was placed on one of these Endorsement pages and it's not supposed to be (not sure if he expected me to correct the entry agent???)

That all said, I would not travel without sufficient space in the passport for all expected stamps, plus some buffer. Not all airlines check, and the risk of getting turned back at immigration is high. If you're in the US, you can contact your rep or senator, sometimes their offices can help for emergency travel doc cases.