I don't personally love the idea of 'training' all children to not express what is basically a biologically natural behavior-- staying near an adult after dark to ensure their survival and protection from predators is a 100% normal human infant behavior. Some babies seem to take to behavioral modifications more easily and comfortably than others, and sleep training can be quick and not as uncomfortable for them, others become so stressed they vomit or become inconsolably distraught and this can go on for many nights.
There are several sleep training options that are not as harsh as crying it out. For example, they could try "The Sleep Lady Shuffle", where the child gradually learns to sleep alone over the course of days or weeks. http://blog.cloudb.com/the-sleep-lady-shuffle-a-proven-way-to-help-kids-sleep/
The other possibility (and really what I think I would do in this particular case) is to just embrace bed-sharing. SIDS isn't an issue with a toddler, who can safely share a bed with mom and/or dad if a few common-sense precautions are taken. This is a personal decision and parenting choice, but when you're at the point of "I'll do whatever it takes to just get some sleep!" or if the baby is just a high-needs, sensitive child who can't tolerate even a gentle training method, I don't think it should be discounted as a reasonable option.
Adding a full size bed to her room where one parent can stay with her might be desired if the 'family bed' doesn't appeal. At least it's better than sleeping on her bedroom floor!