Then they have to use what power they have and simply partition the workload into what must be done that is actually doable and the rest. The rest gets done if there is time, otherwise it just gets dropped.
If the institution wants more work done that there is time for in a normal working day then they simply have to hire more people like any normal company would do. If the institution cannot afford to hire more people then it simply has to admit that there are limits to what it can commit to doing.
This is what unions are for.
That's not how it works in any sort of job with significant individual responsibility. The institution isn't forcing them to do more work. They take it on voluntarily because they're ambitious or competitive or want to advance a worthy cause. Doing the bare minimum is possible: some people make that choice, and even without a union it usually won't get you fired. But those people usually don't accomplish much. You can't have it both ways.