Not true. Most options expire 10 years from grant date regardless of your employment status. This means fully vested option holders have 6 years from grant to exercise.

Yep, and according to things I've previously read, AirBnb switched to RSUs in 2014 and those all have a 7 year expiration date.

I'm only familiar with RSUs in a public company, how can an RSU expire after vest? I thought once it lapses you simply own a share.

Probably some sort of double trigger RSU, where the trigger event is likely an IPO or acquisition.

Taxes. If company is not public, and the RSU converts, employees are hit with 30-50% income tax for the stock value you cannot easily sell.