Even on days when there are strikes scheduled, Trenitalia has what it calls "guaranteed minimum transport services." In other words, there are some trains that will run every day despite a strike so that an entire country doesn't shut down. It's relatively minimal service, compared to normal schedules, and it focuses on commuter hours: 6 to 9 a.m. and 6 to 9 p.m. from Monday through Saturday.
Tickets for these trains can be reserved in advance just like they can be at any time, but of course with such limited service the seats will get reserved quickly. Planning ahead means you might get one of them.