We study the effect of dynamical friction on globular clusters (GCs) and on the stars evaporated from the GCs (stellar streams) moving in the Galactic halo. Due to dynamical friction, the position of a GC as a stream progenitor starts to shift with respect to its original position in the reference frame of initial GC orbit. Therefore the stars that have evaporated at different times have different mean position with respect to the GC position. This shifting results in a certain asymmetry in stellar density distribution between the leading and trailing arms of the stream. The degree of the asymmetry depends on the characteristics of the environment in which the GC and the stream stars move. As GCs are located mainly in outer parts of a galaxy, this makes dynamical friction a unique probe to constrain the underlying dark matter spatial density and velocity distributions. For a GC NGC 3201 we compared our theoretical shift estimates with available observations. Due to large uncertainties in current observation data, we can only conclude that the derived estimates have the same order of magnitude.