The problem is this, once she becomes a U.S. Lawful Permanent Resident and files an I-130 for him, it will take about a year and a half before a visa is available to him and he won't be able to extend his stay in the U.S. and then won't let him back in to visit because he has immigrant intent. So he has two choices:
1) Since the extension request has been filed already, he waits for approval or denial. During that time, your mother can file the I-130 for him after she becomes a Lawful Permanent Resident (LPR). If he is approved for the extension, he stays as long as he can and then if he overstays, he CANNOT overstay longer than 180 days or he will have a 3 year bar that he cannot come back even through his spouse unless he gets a very hard to get waiver. If he is denied the extension, similarly, he cannot overstay longer than 180 days. So basically, if the extension is approved and he decides to also overstay, he would probably be looking at being home waiting for 6 months or a little longer. If the extension is denied, he would probably be looking at staying home for about a year or so.
2) Once your mother becomes an LPR, she files an I-130 for him and an I-131 Re-Entry Permit for her. Then they both leave when he has to leave and she can go with him and the I-131 allows her to stay outside of the U.S. up to 2 years and not lose Residency status. Here is a link to the I-131:
That was, with the second option which is safer, they can be together outside of the U.S. waiting.
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