Recently, I was printing a frame with a tall arch shaped part to it. The designer of the object provides a version with built in support and one without. If I allow Cura to generate the support for the one without, the printing time is a lot less, so that's what I went with.
It was all going well until the support detached from the build plate. The printer then merrily continued, dumping the support material into thin air, where it gradually turned into a big pile of print snot. It is complete coincidence that I was using a green filament.
I trimmed away some of the slot and let it keep going. Amazingly, after a while, the printer managed to re-establish a bridge across the arch with a few layers of support to go, and get to the end of the print.