It is known that the protection from infection in vaccinated persons results not only from the antibody titer, but also quite effectively from the presence of a class 2 T cell response that is extremely sensitive and tends to block access of the virions from the tissue level to the blood stream. This mechanism persists even after AB titers fall below the official threshold.
The same mechanism works in HCV contacts.
Nevertheless, the use of HBIG in this situation is a wise precaution, as well as a booster vaccination.
I believe there is a window period when you can inject HBIG after exposure. Hopefully your own immune system is sufficient to fend off the virus. To a lesser degree, it also depends on the viral load the HBV patient.
I am not a doctor.