Can I lose my house (foreclosed) with 5 years left to pay?

Hi, I'm new to the US (legal), in my home country most people build their homes and are paid off.

I'm confused as to how us housing works.

Say I get a 30 year mortgage for a house, I work hard for 25 years, paying my mortgage, somehow let's say I lose my job, fall ill, or get in some terrible accident where I can't pay my mortgage for some time.

Would I get foreclosed and lose the home I've been paying for 25 years?

Is that how the US system works?

What if it's just one year left?
Added (1). Wow, that's theft. Let's say it's a 120,000 home, at nearly 1 year paid off I get cancer and lose my job, I can't sell if I'm dying at a hospital bed, neither negotiate, and then let's say the bank takes it and sells it, why would they take the entire let's say 85,000 they auction it at, if I would only be left $5,000 dollars to pay?

Why not just take what they are owed and return the rest?

Heck even, triple what is owed, for the "trouble" of auctioning it and take $15K and return the rest?

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