Ask to talk to one of the company's investors if you aren't sure the founder is being upfront about runway. They should have a good handle on the company's cash position (and if they don't, that might be a yellow flag).
Not sure how the relation with investors is in the US, but I can’t imagine them even considering that in any company that I joined. In hindsight, it was a red flag, but I assume there is a cultural gap there.
Depends on stage of company, but for my company (Series A, Bay Area, ~25 employees), we'd be happy to connect anyone with a job offer with our lead investor.