If a mother loose her permanent residency, can she quit claim deed home back to her son?

[minglevi 0]

Here is the possible situation...

 

A son who is US citizen is considering gifting real estate property to his mother who is permanent resident (green card holder)
He is planning to quit claim deed to her and I believe he or her will not have to pay any excises tax as it will be considered gift? I believe he can do as above, please confirm?

Now if by chance his mother decides to give up her permanent residency or forced by agent at airport to give up because she might not come back within 6 months or due to any reason residency is taken away from here...(so now she is not a US person) ....what will happen to property that now she owns (if son transfers as above)? remember when son makes a transfer she is still a U.S. person (Green card holder)

I believe she can still remain owner but after loosing permanent residency (green card) can she still quit claim back to her son in future? Her son will still be US citizen...