Answer
There would be no explanation for the firm to continue its operation.
There would not be a need distinguish between short and long run.
Work Step by Step
If there is no fixed cost, the variable cost would be equal to the total cost. Thus, if the firm is making losses, this would mean that the revenue is less than the cost, and economically, there would be no explanation for the firm to continue its operation.
If there is no fixed cost, there is no need to distinguish between the short run and the long run, as the short run is defined as a time period so short such that not all factors of production can be varied, but in this case, all factors of production can be varied regardless of the definition of the time periods.