The game is amazing, and runs almost flawlessly on my PC. After installation, I didn't even need to fiddle with it, it just automatically ran on my DosBox 0.73. No hard stuff about it, ladies and gents.
But, I did encounter a problem at the very end of the game, DAY 6, "Mooning The Cult".
At the very end, in the stasis chamber, after freeing Eva, when the game switches from gameplay to FMV, it just blacks out. The game is still running in dos box, but there's nothing, no sound... nothing.
So, I restarted, and it ran fine.
But then, when I actually completed the game, after the restart, and the ending FMV began to play, I noticed some lag, and then -- bam! It blacked out again and DosBox did the same thing, kept running, but with nothing on the screen.
I've also encountered random moments where my computer would shut down during gameplay, but I'm pretty sure that just means I need to fine tune my PC. It's been a few years.
I was just wondering if anyone had experienced the same problems. Not much of a biggie, though.
I'm happy with GOG, and with the product they bring at an affordable price. This is ten times better then going on Amazon, and seeing some douche selling the game for $50.00.
Now, let's get "FOXHUNT" into the mix, and my interactive movie wish list will be complete!!!

The only problem I stuck up with the games until now (And I've only played parts of mean streets and UaKM) is that when I change the focus to another window (since I play the games windowed) sometimes the screen locks and takes a few focus changes to get it back working.
But I'm still on the second day of UaKM so I might get into a similar problem in the future. I'll tell you if I get it.

I haven't downloaded the game, so I don't know what version of DosBox is shipped with it.
If it's version 0.72, try replacing it with the newest version (0.73), downloadable from dosbox.com. To replace, just copy the new installation over the old one in the UAKM directory.

I ran into the exact same issue, but did not run into any freezing afterward. Loved how the game just picked right back up where I was beforehand. As much as I'd played it in the past, I never had the situation crop up before and it was nice to see the game gracefully handle it on resume/restart.

One other suggestion is that your install is corrupted somehow, try redownloading and reinstalling the game.
If i remember correctly, after the event you describe the original game required a disk swap. So there might be something connected to the swap that's the issue. I'm not sure how GoG handles the disk-swapping thing ingame. But a corrupted image of that particular disk for example could easily cause a hang-up.

I've just finished UaKM. I ran into the same crash after freeing Eva. Restarted the game, worked fine too. But I didn't run into the other bug.
I'm guessing it's a bug from the original game, not DosBox.

My high end system froze at this same spot, and it repeated so I couldn't get past it, until...I emailed GoG support and they suggested I try all the different settings of the "Graphics Mode Setup" application, found in the game's Start Menu group (which I thought I'd already done), and I was able to proceed with the ddraw setting. It may not work on all systems, so suggest just cycling through them all to see which, if any, works for those that experience this problem.
Cheers!