The photodissociation dynamics of the NeBr2 complex in the B electronic state is studied, for the first time, near the Br-2(B) dissociation limit, below and above, when the complex is promoted from the ground T-shaped level in the X electronic state. A time-dependent treatment is used in which the initial wave packet is divided in two portions, one describing the slow predissociation dynamics below the Br-2 dissociation threshold, and the second one, the fast complete dissociation in Ne+Br+Br fragments. Below that threshold, the absorption spectrum shows an increasing congestion as the vibrational energy content of Br-2 increases, but narrow peaks appear again for the highest energy region of the spectrum. These peaks correspond to long lived resonances associated with "horseshoe" type states, as demonstrated by two-dimensional calculations. These resonances have a significant probability density for the linear geometry in which the Ne atom is inserted between the two bromine atoms. At this configuration the exchange of vibrational energy is rather inefficient which explains both why the spectrum is so sparse and resonances are so narrow. Above the Br-2 dissociation threshold, the recombination of Br-2 is found to be very inefficient, except for very low kinetic energies. The small recombination probabilities are due to vibrational couplings and not to any collisional caging effect. Since the complex remains essentially T-shaped during dissociation, extensive two-dimensional calculations are performed for longer times to better determine final vibrational distributions at low kinetic energies.