When you've got a base +5 to hit points for 10 con, whether your rolling a d4 or a d8 ceases to matter much, and I'm not really sure how you'd fix that.
That's no different from the current situation, and in case you haven't noticed - your hit die doesn't really matter in the face of Constitution modifiers.
The difference between a "-2" and a "+5" is 7 just like the difference between a "+3" and a "+10" would be. Adding a static modifier to both changes nothing except make the degree to which the difference between "2.5" and "6.5" averages on the dice are really small more obvious.
Let's face it, negative modifiers on Hit Dice work even less well.
Consider the way most people apply hit dice and Con changes:
Step 1.: Roll hit die.
Step 2.: Modify it up or down by your Con Modifier, minimum of 1.
Step 3.: When your Con Modifier changes by 1, increase or decrease your hit points by 1 point per level, to a minimum of 1 point per die.
Anybody see the problem?
Let's say a wizard is going to gain a level, but is suffering from some permanent Constitution damage, bringing his Constitution to 1, which gives him a -5 modifier and only 1 hit point per level. So he gains a level, and of course he rolls a die, but the the value is entirely inconsequential as he gains exactly 1 hit point.
Tired of the situation, the Wizard gets his condition restored all the way up to a Con of 10 (or maybe he just polymorphs, whatever). Suddenly, his Con Modifier just went up by 5 - to a total modifier of zero. So his hit points go from 1 point per level to 6 points per level. On d4s, with a modifier of zero.
Under the present situation poison will, in the long run,
make you stronger, because the penalties can keep accumulating past the point where they make any difference and when you go the other way they are bonuses
regardless of whether the penalties were making any difference or not.
Now, when this happens, DMs normally hold their heads for a moment and punt, giving the character the number of hit points they would have had provided that their con modifier had never been low. At least, to the best of the DM's ability to figure that out.
But it's not always possible. Let's take the example of two 5th level wizards, both of whom now have a Con of 10. The first wizard always had a Con of 10, and he has a precisely average number of hit points: 14. The second Wizard had a Con of 9, and raised it to 10 at 4th level, and he rolled the same numbers on all his hit dice. Does he have the same number of hit points?
Probably not. While it is entirely possible to generate 14 hit points by rolling a collection of 2s, 3s, and 4s (2,2,3,3; 2,2,2,4; or of course their 10 combinatorial equivalents), it is more likely that this average result was achieved by rolling some rather more extreme numbers. That is, if there were any 1s rolled along the way, the character who started with a Con of 9 now has more hit points. His 1 result and his 2 result are the same, both before and after raising his Con modifier.
So if the first Wizard rolled 1,2,3,4 - or some similar number scheme - he's got 14 hit points at 5th level. If the second Wizard rolled exactly the same numbers, he now has 15 hit points. He gained, at each level: 3,1,1,2,3 hit points, and then he gained five for the increased Con Modifier.
So the die would actually be more important in the absolute sense if there were no negative stat modifiers - the die would never be overridden by the Con Negative Minimum rule that allows the crafty and the frail to bypass the rolls of the dice entirely.
-Username17