If my mom's husband passed away and before he did he forgot to put her as his life insurance beneficiary, is there anything she can do?

Unfortunately, there is nothing she can do if he did not change his beneficiary designation. If he has someone else named as the beneficiary, she has very little recourse. If he died intestate (without a will) it would be up to the probate court to decide if the monies should go into the residue of the estate to be disbursed. This is the case if he had no beneficiary designated. However, if he has someone else (a prior spouse or a chid designated), that individual or the individual's estate would be the legal beneficiary.