In Person of Interest, the team continues to use the subway tunnel as a "base of operations" even after Shaw is captured by Samaritan operatives. Given that they almost certainly would've interrogated Shaw (which they did), and she was aware of that location, why didn't they find a new location in case she gave them information?
I don't believe this was explicitly stated in the show, but my best guess would be that initially, they believed she was dead from what they saw at the stock exchange, or at least Harold did. Root didn't believe it, but she knew that as Shaw was Indigo Five Alpha, a high-level operative working for the ISA, with training in resisting interrogation (torture), she wouldn't have betrayed their location, just as she didn't break when root was torturing her in her introductory episode ("Relevance").
And finding a new location would be extremely difficult, if not impossible, with Samaritan monitoring everything, it took The Machine to find the subway in the first place and there may not be (m)any other places they could realistically hide with the resources to keep The Machine alive.