SAR IOLTA

If we have an IOLTA account that we are filing a SAR on, would the Law office be a subject, if the activity being filed on was for a
client and had nothing to do with the business itself?

If the law office is not involved in the suspicious activity, it is not a subject. It may be appropriate to list the law office in the narrative if it helps to tell the story of what you suspect. No different than not including a scam victim as a subject even if the transactions passed through their account.

If the client the law office is representing has given them cash derived from illegal activity who is the subject of the SAR?

The client. If the law office is aware and complicit, they would also be a subject (i.e. assisting them with laundering the funds).

If you know that the law office was aware of and complicit with the activity in question, then, yes, you definitely include the attorney/law office.