Is there way for her to fix her immigration status without having to leave the US?

If a mother enters with a visa and her adult USA citizen child sponsors her, normally she would not need to leave.

She may be eligible for adjustment of status if she entered the country with inspection (legally) and has a US citizen spouse or child that is at least 21 years of age who can petition for her.

If your spouse is a U.S. citizen, your mother-in-law can obtain a green card on her child's petition without leaving the U.S. If your spouse is a permanent resident only and cannot become a citizen before your mother-in-law's visa runs out, the process through a petition is still possible, it will just take longer; but your mother-in-law would not have to leave the U.S. Finally, she should talk to an immigration attorney about her fear of returning to her own country: it is possible that she might have a viable claim for asylum in the U.S.

If your mother in law came to the US with a visa, (even if long since expired) she may not have to return to her country to visa process if she is an immediate relative of a US citizen who can file petition for her. In this situation, if your husband, her son is a US citizen, then, he should file a petition for her. I caution that in filing any thing with immigration, you need to consult with an experienced immigration lawyer, because, several requirements must be met in addition to being a mother of a US citizen and unless all of those requirements are met, she may still be ineligible for a green card.

More facts are needed to analyze this case. I suggest you set up a consultation with an immigration attorney- many of them offer free consultations.