If my mom holds a green card but doesn't reside in the US, is she ok to come here on her green card?

It depends on how long she has been outside the US and whether the green card status is still valid or whether it has been terminated due to abandonment.  A green card holder cannot remain outside the US for more than 6 months without jeopardizing one's green card status.  She may have the physical green card in her possession but it may have been terminated and if she attempts to enter, she will be detained.