  We propose a new approach for studying the neutron star/supernova remnant
associations, based on the idea that the supernova remnants (SNRs) can be
products of an off-centered supernova (SN) explosion in a preexisting bubble
created by the wind of a moving massive star. A cavity SN explosion of a moving
star results in a considerable offset of the neutron star (NS) birth-place from
the geometrical center of the SNR. Therefore: a) the high transverse velocities
inferred for a number of NSs through their association with SNRs can be
reduced; b) the proper motion vector of a NS should not necessarily point away
from the geometrical center of the associated SNR. Taking into account these
two facts allow us to enlarge the circle of possible NS/SNR associations, and
could significantly affect the results of previous studies of associations. The
possibilities of our approach are illustrated with some examples. We also show
that the concept of an off-centered cavity SN explosion could be used to
explain the peculiar structures of a number of SNRs and for searches for
stellar remnants possibly associated with them.
