It should have been in your tenancy agreement that the tenants are responsible for paying council tax. If they do not pay the LA will go to the Magistrates court and obtain a liability order this gives them the authority to take action for non payment of council tax which in your instance will probably have been passed to a firm of private bailiffs, collection of council tax is a major form of income for private bailiff companies. If payment is not made when the bailiff calls on the correct people and they gains access by peaceful means they can size goods (statutory distraint) and sell them to recover the amount owing plus their charges.
If you are not named in the liability order no action can be taken against you. I suggest you write to both the LA and bailiffs and explain the position all action should then cease.