I claimed Mom on my taxes, now she may go into nursing home. Will they want me to pay for the nursing home?

As far as I know, the filial responsibility laws have not been used to deny Medicaid to residents of any state. As CMagnum pointed out, the fact that you claimed her as a dependent does not mean that you are responsible for paying for her care. If her own funds are insufficient (and almost everyone's are), you should start an application for Medicaid as soon as it looks like she may need to enter a nursing home.

Look it up and see. Unless she has long term care insurance, her other insurance will not pay for the nursing home.

We live in Mass and I understand that there may be a filial piety law? She has Mass health and Unicare for Insurance.

Just because you claimed your mother as a dependent on your taxes does not mean that the nursing home will want you to pay for it, but someone will. Maybe you need to see if she qualifies for Medicaid.