I am familiar with different terminology. What you call precision I would positive predictive value (PPV). And what you call recall I would call sensitivity (Sens). :
In the case of sensitivity (recall), if the denominator is zero (as Amro points out), there are NO positive cases, so the classification is meaningless. (That does not stop either TP or FN being zero, which would result in a limiting sensitivity of 1 or 0. These points are respectively at the top right and bottom left hand corners of the ROC curve - TPR = 1 and TPR = 0.)
The limit of PPV is meaningful though. It is possible for the test cut-off to be set so high (or low) so that all cases are predicted as negative. This is at the origin of the ROC curve. The limiting value of the PPV just before the cutoff reaches the origin can be estimated by considering the final segment of the ROC curve just before the origin. (This may be better to model as ROC curves are notoriously noisy.)
For example if there are 100 actual positives and 100 actual negatives and the final segnemt of the ROC curve approaches from TPR = 0.08, FPR = 0.02, then the limiting PPV would be PPR ~ 0.08*100/(0.08*100 + 0.02*100) = 8/10 = 0.8 i.e 80% probability of being a true positive.
In practice each sample is represented by a segment on the ROC curve - horizontal for an actual negative and vertical for an actual positive. One could estimate the limiting PPV by the very last segment before the origin, but that would give an estimated limiting PPV of 1, 0 or 0.5, depending on whether the last sample was a true positive, a false positive (actual negative) or made of an equal TP and FP. A modelling approach would be better, perhaps assuming the data are binormal - a common assumption, eg: