Yep! And that's exactly what I didn't encourage them to do. Or rather, I suppose I went about it the wrong way. For example, at one point one of my players got really invested in freeing a group of exploited clone secretaries. I was building towards consequences for that, but it never came to fruition. Also, I tied too many PCs to a single bad guy, and when he died, the game kind of stalled out when the rest of the PCs didn't have a backup motivation. So I guess the lesson there is that in a sandbox game, make sure your PCs want to have a long-term impact on the setting.
But see, I did that. The NPC was like, "Y'all go take out all those pirates now, y'hear? We'll pay y'all so much more money. And some nice upgrades fer y'ship!" And then they got a starting point to go pirate-hunting, and then...nada. Bupkis. Zilch.
What I suspect happened is that this is roughly where their motivation died. They realized that pirate-hunting was fun, but ultimately nothing they could really invest in. And that's when the campaign broke. Now, if they'd had backstory hooks about a pirate crew that had destroyed their family, then at least one of the PCs could have been invested! But as previously mentioned, I tied too many players to a single BBEG and then they did the thing that PCs do - and wiped out a whole continent trying to get him (it was ugly).