See – here's the thing… You can't just say "in my tabletop game." There are 10,000 tabletop mechanical systems, each of them with slightly or extremely different mechanical expectations, processes, and outcomes.
I know, it's hard to imagine there are other games than D&D out there – but I assure you it's true.
But let's look at the specific mechanics you just mentioned and think about how they can be useful and applied narratively.
(And even this description leaves open some really potentially horrific possibilities, like the question of whether you must actually ingest the healing potion material in your intestine/stomach before the healing occurs or does rubbing it on your skin suffice? Does inhaling it count as indigestion? It doesn't necessarily have to be so. The processes of drinking and breathing don't often crossover.
But leaving all that aside…)
Assuming a character with 50 HP and drowning damage of 1d10, just for the sake of argument. Your average damage per turn is 6 which means that character will drown, on average, at -100 HP, which gives you an ETA of 25 turns. If your turn length is 6 seconds (which is pretty classic), you have drowning occurring in about 2.5 minutes.
In order to be able to drowning in a vat of healing potion, the healing rate needs to be lower than the drowning rate – so let's say that one dose of healing potion only restores 1d6 HP, so on average 4. The last, on average, your character will lose two hit points a turn, thus will drown in about 75 turns or 7.5 minutes, about three times as long.
The linear arguments in this very approximate description are quite broad, which is fairly common with single die resolution mechanics. The wider the potential swings, the more variability. But let's think about what that says as described.
Effectively, you can only drown someone if the healing rate is less than the drowning rate. Otherwise, you can never keep up. Most healing potions as described in fantasy games are contained in extremely small vials, so a vat would be an incredible number of doses. As such, you would end up with a corpse floating in a relatively significant vat of potion as a result.
If the healing rate of the potions is higher than the drowning rate, and the rate of production (which you assume has to occur since were floating in a vat of healing potions) is sufficient to keep the vat deeper than the height of the character, you could keep them in a state of continual drowning for as long as you can maintain production.
Want to drive someone insane in a particularly ironic way? Chain them down/wait them down in a vat of healing potion in a healing potion factory; watch as they drowned for all eternity.
Want to make a particularly potent or necromantic healing potion? Maybe the preparation process involves drowning one or more people in the potion in order to empower it? Binding them face down in the container might make it easier to consume their life force in such a manner. Using babies is advised!
Who even has an entire vat full of healing potions? What kind of industrial magical processes are required in order to produce that much of a valuable material, one that any Empire, kingdom, or significant military force would love to have their hands on? Is that potion now completely spoiled – or will whoever owns it end up using whatever's left because it is so valuable, and is there going to be some sort of magical residence repercussion?
Honestly, the potential story around such an event is more interesting than the question itself. "What can I do with this?" should always be on your mind.
I suppose by "In my tabletop game" I was specifically mentioning my D&D 4thed game where the question specifically came up. It was a pretty homebrewed game though, tons of fun
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