Just to clarify things, the Udemy free offer courses that I have seen don't expire once signed up during the free offer period. They aren't bait and switch tactics, more promotional to get people to view and review the courses and get likes etc, much like a restaurant giving free meals.
I've been using them for quite a while and never paid a cent as most of topics I'm interested in come up from time to time with a free course, some of them are quite comprehensive but don't expect an engineering degree here.