Nobody gets removed, they just have to leave. It's a subtle distinction but that's how it happens. Poor people don't own anything. Their furniture is mostly stacks of junk that is so bad that it would be hard or impossible to get someone to accept it for free (this is very nearly a tautology, since the poor person got this furniture for free to begin with, and it's was so bad when they got it that nobody else would give anything for it). They rent. At some point property values are high enough the landlord (or his heir) decides to sell. At the end of the lease, the property is no longer for rent. That's the end of it. However, keep in mind that poor people tend to move every few years regardless. They are right on the edge of falling out of the population of working people who are self sufficient, so it is very common that they end up being evicted, abusing drugs or alcohol (even if just for awhile), or just having too many kids to be able to afford childcare so they can keep working to support themselves. Properties no longer being for rent in some neighborhood has almost no effect on any given poor person who lived in that neighborhood as they are one step above transient anyway.
This isn't an apology, it's just a more accurate description of what happens, I've seen it first hand from the low prestige side of things when I was young.