How to run old 32 bit linux software in a container inside a modern 64-bit distribution

I need to create a container to run an old proprietary software that used to work in my old 32 bit computer with Ubuntu 8.04. I have been adapting this software in successive OS upgrades by linking the required libraries to the modern versions, but now it has reached a point where I cannot do that any more (not at least easily). But, with Playonlinux it is possible to create a container with special libraries and an old Windows program will "believe" he is inside Windows 3.11 for instance and will work, unaware that he is in an alien world, a linux 64 bit machine in 2018... If that is possible, adapting my linux 32 bit software should be easier if only one knew how. Words like "Fakeroot" come to my mind but I don't know where to begin. Even when a complete answer is not possible, clues to start with are welcome. PS. I'm using Debian 9