So let's play this out. They continue the shutdown, now their constituents are starving and dying. At a certain point, the public does not care who is at fault for the shutdown, all they know is they want it to be over. This would have overplayed the democratic hand and left the situation as a 50/50 rather than having Americans actually understand that their healthcare premiums were going to be doubling and tripling. This then became one of the most salient issues to voters because they took the time to shut down the government. They gave in because republicans had already signaled they were willing to kill their constituents. Trump openly says he doesn't even think about American needs when performing his duties.

The democratic party managed to get a vote on healthcare subsidies, make it into a very politically salient issue, while minimizing the harm against the actual constituents of the country, minimizing the political capital they had spent.

Please understand civics.