-I guess your mon's status is B2. if so, no grace period.
What can we do if we don’t want her to carry this bad record.
-Your mon should have filed her status extension application before the I-94 expired. It is too late now. She had better leave U.S. as soon as possible, otherwise she will be not be allowed to enter U.S in three or ten years if her unlawful presence > 180 days or one year. If you are US citizen, you can sponsor her to apply for GC and she can continue to stay in US and after she gets GC, she can go out of U.S. and come back with a problem.