Why's a penny stock basically a call option with a strike price of 0 that doesn't expire? This Reddit comment proclaims:

A penny stock basically IS a call option with a strike price of zero that doesn't expire.
I suspect there's a high correlation between penny stock investors and people who buy deep OTM options hoping for a home run.

I understand the concept of a call option that doesn't expire, but I don't understand &quot;strike price of zero&quot;. Though penny stocks can $\rightarrow 0^+$, they must $\in (0, 1)$. So why would the strike price be 0?
Your misunderstanding comes from the fact you are treating a penny stock as an option. They are not the same this is just a metaphor. The difference that makes the difference here is ownership.   

The reason the strike price would theoretically be zero is, for a penny stock you own the underlying asset, so you would not pay to own something you already own. A strike price is how much you need to pay to purchase the asset, but you own the asset in this case.

The OP Reddit poster is dead wrong and is referencing a huge amount of underlying assumptions about penny stock trading and options trading. You can't treat them as the same.