***Or Can they leave immediately after entering the USA every year and maintain the GC status?*** There is a purpose that green card serves...and it is that it allows you to maintain status as a permanent resident of the US. You can try leaving the US immediately after entry, but the entry officers are not foolish either -- be prepared to be questioned and provide to them a proof of non-abandoning US as your primary residence. Also, remember that there is *never* a guarantee that you will be allowed to re-enter the US... that right is reserved for US citizens only, regardless of whether you have a valid visa, AP, or a green card.