If I don't pay my mortgage, my home gets foreclosed. If a tenant doesn't pay rent, they're evicted. How can someone "not afford" their living expenses, yet simultaneously live there? As is the case with millions of people in Singapore?

Your point about real estate is spot on. As prices rise, fewer can afford it, so they leave. So according to this logic, if 5 million+ people live in an area...

Singapore's population is just now starting to decrease, so yes, so some people, it appears its becoming unaffordable.