According to the theory, when quantum fluctuations occur near the event horizon, one is absorbed and the other is emitted as hawking radiation But in order to conserve the energy the fallen particle must've been of negative mass We know that negative mass particles move in the opposite direction of the acceleration applied to it, so how can that negative mass particle fall into the black hole in the first place?
The description of Hawking radiation as a particle - antiparticle pair being produced near the horizon is not entirely accurate.
It may be better to think of it in terms of the Unruh effect, which states that an accelerated observer will see blackbody radiation where an unaccelerated one will see nothing. Near the horizon, an observer must accelerate to keep from falling in. Thus they will see a thermal bath of particles that arise from the horizon and fall back in. However, we also require local thermal equilibrium. Therefore some of this particles must escape to infinity.
This answer may prove useful for you. It is better to not think in terms of mass flux and rather energy flux. There is a positive energy flux to infinity, so there must be a negative energy flux (relative to the exterior) that falls into the black hole. This leads to evaporation and the usual consequences of Hawking radiation.
This is a wrong statement:
But in order to conserve the energy the fallen particle must've been of negative mass
Real particle pairs have real masses, for example an electron positron pair each particle will have a mass of about .5 MeV. The energy for the masses creation + kinetic energy is provided by the gravitational energy of the black hole. That is why one says that black holes "evaporate". They lose gravitational energy by Hawking radiation.