I've got some tender bulbs like pineapple lilies and some amaryllises that do that slimy, mushy phase before drying. I think its due to such big, water filled stems. It does appear alarming at first, but I've never had any of them develop rot issues as a result.
Several of my tender potted bulbs have to come inside before the foliage has been frosted. I let them remain dry and allow the foliage to gradually dry and die off. Usually takes about a month to 6 weeks for all the leaves to dry.