How (or whether) any non-RSUs are handled is always part of the deal. The good thing, is that an RSU is an RSU... and execs with way more than you have the same types of RSUs and regulations wont let them be handled differently (IE, someone on ELT cannot vest immediately and you get nothing)....
Now with that said, there are a number of ways of it going down. One is if the acquiring company is a private org, they COULD vest you and pay it out. Of course they could also convert it to the dollar value of the shares and keep the vesting schedule... Meaning if you have 50K vesting next year, they just turn that into equivalent cash bonus that you must be employed there to get.
If its not a private equity company, then they will have their own shares. So public companies (like MS lets say) have the option to convert your RSUs to their shares that vest on the same schedule. So its pretty close to option 2 listed above.
What happens? no one knows. It all depends on any deal struck. anyone that says they know is guessing. any number of options is available to the acquiring company...
Of course they could fire you at acquisition and you and any unvested RSUs are lost.