I am ready the new contract between my company and our union, and in the section about how the union reacts to an unauthorized strike, it says:
The Union shall promptly order its members to return to work notwithstanding the existence of any wildcat picket line
What is a wildcat picket line?
well, a wildcat strike is a strike without the approval of union leadership. http://en.wikipedia.org/wiki/Wildcat_strike So a wildcat picket line is presumably a picket line made up of participants in a wildcat strike.
Most commonly, it means an illegal strike – a strike called while there is still a valid contract that binds the union. Less commonly, it’s a strike not at the behest of union leaders.
Wildcat pickets and strikers are any workers who are not acting under the direct association with the union. A wildcat strike is typically one in which the workers at a particular shop decide to walk out even though they have either not sought support from the union or have chosen to ignore the union when it said not to do so.
In the clause you reference, it would seem to mean that the company will expect occasions when the workers would continue to picket even though there was no work stoppage (off-shift workers standing in front of the plant holding signs). In this case, the union agrees that workers who refuse to cross that (unauthorized) picket line may be punished for failing to show up for work.