Methods for producing glass articles from laminated glass tubing include introducing the glass tubing to a converter. The glass tubing includes a core layer under tensile stress, an outer clad layer under, and an inner clad layer. The methods include forming a feature the glass article at a working end of the laminated glass tubing and separating a glass article from the working end of the laminated glass tubing, which may expose the core layer under tensile stress at the working end of the glass tubing. The method further comprises remediating the exposed portion of the core layer by completely enclosing the core layer in a clad layer. Systems for re-cladding the exposed portion of the core layer as well as glass articles made using the systems and methods are also disclosed.