Sales taxes are also trust taxes, just owed to the state. I would start with CA and see how they handle delinquent sales taxes. I had a similar situation in PA with an S Corp, except it was active and my tax client. I contacted the state and they said to file the returns and they would want payment, but the client could probably drag it out 6-9 months. My client could not pay it in 6-9 months and PA does not easily offer payment plans in general. I ended up referring it to a tax attorney and he told the client to file the returns and he would assist when the notices came.
So I would start by contacting the state and seeing their policy on back sales tax. I don’t know if they can come after the partners like they can with payroll tax.
Sorry if this was not helpful. Post what happens though. I would like to learn.