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The simple answer is yes it's possible, if they have a suitably developed physiology. Vampire bats, leeches, mosquitoes and more are proof of that. There are complications that make it less practical than you might want though.

Lets start from a Vampire Bat (as a mammal it seems a good starting point for comparison). From wikipedia:

A typical female vampire bat weighs 40 grams and can consume over 20 grams (1 fluid ounce) of blood in a 20-minute feed. This feeding behaviour is facilitated by its anatomy and physiology for rapid processing and digestion of the blood to enable the animal to take flight soon after the feeding. The stomach lining rapidly absorbs the blood plasma, which is quickly transported to the kidneys, and on to the bladder for excretion.A common vampire bat begins to expel urine within two minutes of feeding. While shedding much of the blood's liquid facilitates flight takeoff, the bat still has added almost 20–30% of its body weight in blood. To take off from the ground, the bat generates extra lift by crouching and flinging itself into the air. Typically, within two hours of setting out in search of food, the common vampire bat returns to its roost and settles down to spend the rest of the night digesting its meal.

So this suggests that they consume half their body-weight in blood every day and digest it. It also suggests that being near a feeding vampire would be unpleasant as they need to quickly dispose of the liquid waste from their feeding.

The maximum a human can lose without serious risk is 3 litres. 1 litre is the maximum than can be lost without side effects.

If we go with the "half your body weight" formula then even a lightweight 50kg vampire would need to consume 25kg of blood. Since 1kg of blood is the approximate weight of 1 litre the vampire would need 25 litres of blood per night.

That's draining to death 5 people or partially draining 25 people. Per night!

Now if the vampire was not flying and/or had a lower metabolic rate it might have lower energy requirements. If rather than scaling a vampire bat up we looked at a human we can see that your average adult human needs 2000 to 3000 calories per day. A litre of blood contains 600 calories according to some Google searches that are going to look interesting in my browser history. We're going to assume that there are enough raw materials present as well as the calories to allow any missing resources to be synthesized.

That gives us a lower figure of 4 to 5 litres needed per day. That's more manageable but still seems like a hard thing to hide. We're now talking 1 death or 5 living victims per night.

It's seems far more likely the vampires would go after herd animals such as cows than after humans. Cows contain more blood, tend to be more exposed at night, and will ask fewer questions.

The mess made from expelling the waste will also be less likely to be noticed in the middle of a field than in someone's bedroom!