There absolutely is. There was a successful nursing strike in Worcester, MA that lasted 10 months and the hospital didn’t shut down. It was staffed by a rotating cast of expensive travel nurses.
It’s a controversial maneuver because it can prolong a strike, but it maintains public support and also prevents possibly endangering the lives of people in the community, which is the opposite of what we’re trying to achieve in a healthcare strike.
(Personally, I am firmly of the belief that if any service is so critical to the public well-being that a compromised strike is necessary, then that service should be owned by the public and not a corporation. But that’s a whole other conversation.)