Can a relay failure mode be like that?
The type shown is a flux-sealed type. It is frequently recommended that such relays be vented after the soldering and cleaning operation (if any) in order to extend the life of the relay. This is because it allows contaminants caused by the wearing contacts to escape during the relay life that would otherwise be trapped inside. 

Presumably the relay that wore out was switching higher current than the others, so it was deemed important to not only open the vent, but to mark it with a Sharpie so that inspection could check it. 

Here's a section from a different datasheet from the same Taiwan-based manufacturer: 



This may be indicative of a problem that the appliance manufacturer has been having and subsequent recommendations from the relay maker.