Way to not answer the question.
You asked a loaded question that is not based in reality. You suggested all the houses being bought up and no more houses left for anyone else to but. this scenario is as absurd as suggesting all the cars bought up by the rich to the point that there is no more cars left for anyone else to buy, greed and opportunity would never allow that to happen
But to answer your questions/statements what happens as people run out of room to build more housing?
We would run out of roads to drive cars on before we run out of room to build more housing.
What about people who can't afford to rent, what help do you propose for them?
Buying is far more expensive than renting, so renting nor buying is an option for them, they will need the government to step in to help them.
How did there get to be people who can't afford to buy if not through the rich hogging an unnecessary lions share of money which we can't afford to live without in the first place?
First of all, the rich have very little money; they give the vast majority of their money to corporations in exchange for company shares; and those companies use their money to make payroll, research and development, invest in technology, and other company business required to remain in business. So if you don’t have enough money, go to the companies who have most of the money, and they will share some of their money with you so long as you agree to do work for them.
Ok, but I believe assessing whether a person can afford a few squatters or not would allow an easier eviction process for those who couldn't afford it.
No; the only way that would ever happen is if squatting becomes common which it is not. It is extremely rare for this to happen.