The behaviour of dice loss when target and prediction are disjoint

I’ve been struggling with the implication of the dice loss value generated when t (target label) and p (predicted label) are entirely disjoint. Dice score being (2pt)/(p+t), this value is zero (or very close with epsilon being involved) for all disjoint but non-empty t and p. The derivative of the dice score is (2t^2)/((p+t)^2), which means that there is still gradient when t and p are disjoint, provided that t is not empty. Does this mean that dice performs poorly from a training standpoint as a loss when t and p are disjoint or does it just mean that it isn’t informative as a metric (i.e. that dice loss returns 1 due to dice score returning 0 as its numerator is always zero when t and p are disjoint)?