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First up, most models aren't made with carpal bones. In reality, the width across the hands/knuckles can change slightly. Not enough to notice for most game animations, but definitely enough to notice for a fist.
Secondly, limitations in how bone posing can deform an object. Because a model bone needs to deform at least a little of the surrounding area to make the transition look natural-ish, you end up with the base of the fingers actually trying to push apart when you bring them together (a side effect of wanting it to stretch when they move apart). More than that, Source's skeletal animation cannot maintain mesh volume in the same way as some more sophisticated programs.
Without corrective morphs (which are a very little explored and not properly supported science in Source), there have to be compromises.
TL;DR: The models aren't well designed and you're using an old game engine.
Adjust the fingers to close the gaps, switch to Local Rotation mode, select all the finger bones Less the Thumb bones, rotate on the axis that turns them into the hand. Then adjust the thumb. After make minor adjustments if necessary. Animating, just do the same thing while you have the time line offset for the amount of time you want to make the fist...
If your working with a model where the bones aren't nice, same thing, except do each finger separately and adjust for the bad bones.
https://i.imgur.com/NjdV1rl.gif
https://i.imgur.com/k7d1B6q.gif
I mentioned it already. I tried it. I said they get to the palm before they can curl. Depending on the model
You know what I ACTUALLY did that though I wasnt sure if it was a requirement cause it worked but it did something to the knuckle that I think wasnt legit but it could be me. It made it simpler just wasnt convinced thats how a hand works XD I guess I think too realisticly for animation