...but no self-respecting troll would want such a wretched life.
A troll can sustain almost limitless stirges
A stirge (MM 284) takes on average two attempts to hit a troll (MM 291), dealing an average of 5 damage, and draining an average of 5 hit points worth of blood until until it has drained 10 hit points. Since the troll regenerates 10 per round, he can sustain two feeding at a time indefinitely.
In theory, the troll can regenerate enough each day to feed 9,600 stirges, given that there are six seconds in a round, 86,400 seconds in a day, the troll regenerates 10 per round, and each stirge deals 15 damage to feed. This is a hypothetical maximum and doesn't account for the practical logistics of moving this many sitrges around.
In practice, the stirge's instinct is to swarm its prey in large numbers. In this case, twenty Tiny creatures can surround a single Large creature, not even considering three dimensions. On average half will hit in the first round, dealing 50 damage, of which 10 will regenerate. In the subsequent round, the attached stirges will drain the troll of enough blood to reduce it to 0 hit points.
However, a stirge only detaches when the creature is dead, and the troll is not dead at 0 hit points. Thereafter the troll remains in a constant loop of regenerating 10 and being sapped for 10 either by suckers or new joiners.
According to The Ecology of the Stirge by Ed Greenwood (Dragon Magazine #83), the stirge eats once every 72 hours (3 days), and will starve after another day if it cannot feed. Therefore, a troll can support a theoretical maximum of 28,800 stirges, or 38,400 if they all wait until the last possible moment to feed. Again, this is only a theoretical maximum, and would be impractical in reality.
However, we must also consider the possible mutations which will occur when a troll is subjected to such an ordeal over the long term (MM 291):
Their regenerative capabilities make trolls especially susceptible to mutation. Although uncommon, such transformations can result from what the troll has done or what has been done to it.
The troll may mutate a harder hide or poisonous blood to stop the stirges, or it may start to produce even more blood to feed its swarm. This would, of course, by up to the DM to speculate on.
Do stirges reproduce fast enough to sustain a troll?
The troll is described in earlier editions of D&D (particularly the D&D 3.5 Monster Manual) as weighing 500 pounds, around the same size as a male lion, similarly a predatory carnivore. A lion eats up to 66 pounds of meat in one session and requires around 15 pounds per day.
However, trolls are "born with horrific appetites", and are not described as having the lion's feline habit of resting for up to 20 hours per day. While there's no fixed definition of how much a troll eats, Dragon #301's Ecology of the Troll says:
Much of their activities focus on acquiring food, whether exploring their habitats for sources of meat, preparing ambushes, or actually tracking prey.
We can infer that the troll eats considerably more than 15 pounds per day, but the exact amount is unknown. It is much more active than the lion and would reasonably require more energy, but the exact amount is not specified.
There's no reference that says a troll who regenerates becomes hungrier. The third edition Monster Manual says its regeneration is not magical or supernatural in nature, so it could be a biological process which requires energy, but even in that edition it's not explicitly stated as such.
An average a stirge is one foot long (Dragon #83). Supposing its weight is similar to that of a winged animal of similar size and shape, the grey-headed flying fox](https://en.wikipedia.org/wiki/Grey-headed_flying_fox), which has similar wingspan and length, it may weigh around 2 pounds.
Considering that our troll probably eats at least twice as much as a lion, at a conservative estimate, he would need to eat at least 15 stirges per day, and it would not be at all unrealistic for the troll to eat 30 or 50 per day.
Unlike the troll, the stirges have no fast regeneration (although Dragon #83 suggests that they can regenerate wounds over a period of days, or missing body parts over a period of months). We're reliant on their breeding rate to keep the troll fed.
As per Dragon #83:
They reproduce by live birth, in litters of one to three young, with a gestation period of six months.
They become adult size after another seven months.
In optimal circumstances, a swarm of 100 stirges would produce on average 200 young each year (assuming 50% female producing an average of 2 offspring every 6 months). This isn't accounting for stirges which die of natural causes or are eaten by a troll.
Unfortunately, we don't have figures for the stirge's lifespan. However, based on its description of infrequent reproduction, long pregnancy, long period of parental care, and relatively low number of offspring, the stirge surprisingly sounds like a K-selected species, who tend to have relatively long lifespans.
It's possible, then, that the stirge has a natural lifespan as long as ten or even twenty years, especially with a limitless supply of food. Barring disease, accidental injury and the like, we may be looking at a growth rate of over 150%.
Assuming the troll needs to eat somewhere between 20 and 50 stirges per day, a colony of stirges would need to produce anywhere from 7,300 to 18,250 offspring per year to satisfy the troll's hunger.
This is within the possibility of the troll's ability to feed the stirges, but with three caveats:
- The troll would need to spend a substantial amount of time lying around in a weakened state being bitten by stirges.
- The troll would need to have an absolutely massive colony of stirges. They would fill an entire cavern and the sound of their wings would be deafening. Stirges (according to the 3.5 Monster Manual) tend to live only in groups of 12 or so, and breeding the necessary 3,000 or more over the course of five or six years (without eating any) would be time-consuming and require patience which is not typically attributed to the troll.
- The troll would have to go against his instincts of hunting large prey, and perhaps any religious teachings of Vaprak the Destroyer. Other trolls who learn of the stirge cavern would not only find his lifestyle immoral, they would also take great interest in eating their way through a massive store of delicious stirges.