These are fast growing poplars. They are very popular up here, pardon the pun, as even in our harsher climate they just grow and grow. If you can find a tree anywhere, they are prone to shoots, which are very easily transplanted.
My brother and his wife were faced with a dilemma a few years ago. One morning they woke up to find the green space behind there house had been cleared bare, in preparation of the proposed high wire electrical stuff the province was installing. So, they scrounged around for some shoots, and bought 25 seedlings. Two years later, these scrawny things are 10 feet high.
If you can get a some maturer trees, this could be a better idea than bamboo as it's not nearly as invasive.
As I understand it, the roots are very strong and can and will probably break right through the remaining foundation, provided you add a wee bit more dirt on top of what you've got.