Biting can be a serious problem in a pet rat, although it's extremely uncommon and extremely rare that a rat is going to develop a biting type of behavior. It does definitely happen. In the majority of time, this is rat that has not been properly socialized. It has not been handled from the time it was very young, or it's a rat who's personality is just being skittish and being fearful, and it tends to be more of a fear biter then an aggressive biter.
In these cases these rats one: Are important to know that they are biters to be prepared and to warn other people. They're also important to work towards trying to decrease the behavior and potentially eliminate it. Many people have found that with time and patience, learning techniques to work with the rat, understanding when and why they may be prone to biting, that they can actually desensitize the rat from becoming a biter or from continuing the behavior of biting and get them to the point, where the rat will actually trust them enough to not feel the need to fear bite.
Basically, it requires a commitment, time, and patience, and the desire to actually have this rat become one that's not going to bite or nip for no reason. Oftentimes, people learn that they can use bite-proof gloves or they can use a hand towel, or something on the rat to prevent them from being bitten while they work with handling, desensitizing them and getting them used to not having to be fearful. The biting is not a very common problem.
In most cases, if a rat is a biter somebody is warned about that or somebody has learned. Hopefully, they let other people know. As well as, let people who may potentially handle the rat know so that you can take extra precautions to deal with them, and also work with training them out of the behavior that probably started when they were very young. It may be difficult, but in most cases, you can work towards developing more a more trusting bond.