When emptying the milchig dishwasher, I found a ceramic mug that I keep with fleishig dishes, that is used to drink tea or pareve coffee after fleishig meals, when the person drinking it is “still fleishig”. It is possible, but not common, that actual fleishig food or soup ever got into that mug, but certainly not on this particular occasion, and not any time in the recent past. I assume that there is no problem with the dishwasher or any other items that were washed that cycle, but what is the status of the mug?
The status of the mug, if it did become milchig or not would depend on the type of dishwasher the you have, and what it was washed with. However even if the mug did get some milchig taste in it, you are not really using the mug for fleishig, rather for when you are “fleishig”. Therefore, you can continue using the mug even for drinking after a fleishig meal.