Traveling outside USA while Visitor Visa (B2) extension application is pending

[mowgli1]

My parents' stay in the US expires in about 45 days. I would like to file for an extension application so that they can join me for a cruise vacation to Western Carribean. This vacation date is after their current stay expires. If their extension is not processed by the vacation date, can they travel outside US for this vacation? Would there be any related risks we should be concerned about?

Also, I have a citizenship application currently pending. If I become a citizen, can I apply for my parents' permanent residency during their visa extension period stay in the US? Can they travel outside US while their permanent resident application is pending?

Thanks a lot in advance for any advice!

[immihelp]

1. Yes, they can travel outside the US.
2. Yes, you can for their green card as soon as you are US citizen, even while their B2 extension petition is pending.