Can a TRIAC fail closed?
Fail-closed is the usual failure mode for power semiconductors, triacs, diodes etc. An overcurrent event will tend to overheat the semiconductor, which melts everything into a highly doped and therefore conductive mess. An overvoltage event will tend to punch through insulation layers, with much the same result.

This is why you always use a fuse in the input to a bridge rectifier supplied instrument. If one diode fails, it's likely to go short, which will then take out its opposite number, also short, shorting the input.