It depends a bit on your state specific laws, but a lot of states cover auto-related injuries off of your optional medical coverage(med pay), or even state required PIP(personal injury protection). Your liability or uninsured/underinsured only applies if you are in the car in general, but those med pay/PIP coverages are a lot broader. We've had people covered by those who were working underneath their car and it fell on them, rolled over their foot, and all sorts of crazy stuff when they weren't actually in the car. I would assume the med pay/PIP coverage probably wasn't anywhere near the amount of your full liability limits (might be something like 5K or 10K when your liability is 100K or whatever). Again it depends on state laws, but I dont think insurance companies generally seek to recover PIP/Med pay payments.
It's hard to say if your insurance company would have gone after the other driver personally once his insurance limits were exhausted. Some of it might depend on what his actual limits were, and what they realistically thought they could get out of the guy. If you work a minimum wage job and have no assets, they probably won't bother coming after you, regardless of what your insurance paid. If you have a 6-figure job and a lot of assets, you better have some very high liability limits, because they'll come after you if your insurance isn't enough coverage. Insurance companies aren't dumb. They aren't going to waste the legal cost of suing someone if they know they don't have any way to realistically pay the damages assessed against them, they aren't in it for moral victories or anything of that sort. They're only going to be suing someone personally if they obviouslly have enough money to possibly pay what they think they will be awarded.
We try to stress to people all the time who we know have a lot of income & assets that they really need high liability limits, or even an umbrella to protect them. You don't want to be sitting there with hundreds of thousands, or millions of dollars in assets and only $25,000 liability on your vehicle. Hell, at that point even $100,000 isnt enough to protect you. In most states you can get a million dollar umbrella policy for a couple hundred bucks a year, it's stupid not to if you have a good income and are pretty well off. It's a pittance for protection from a lawyer coming after you for everything you have if you hurt someone really bad.