We examine the possible role of stress-driven surface instability in the failure of electric interconnects found in large-scale integrated circuits. While electromigration is commonly known as the main reason behind interconnect failure, the complex interplay of electromigration-induced mass transport and stress-induced transport has also been studied extensively since the discovery of the Blech effect due to its importance in integrated-circuit design. However, the role of the dielectric medium confining the interconnect has not been properly included in previous analysis of this phenomenon. Here, we examine the classic ATG instability in the presence of dielectric confinement. We propose that thermal stress and surface transport, typically active in all metal interconnects, may trigger a surface instability at the metal-dielectric interface. In particular, we show that there exists a critical thermal stress level below which the stress-driven surface instability cannot be responsible for the failure of interconnects of any length. However, for an interconnect confined by soft low-k dielectric materials, thermal stresses can still be large enough that such stress-driven instability may break the metal conductor even if its length is below the Blech limit.