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Quite an unusual behavior of the low-energy ion fluxes measured with the LECP and CRS instruments onboard Voyager 1, which is located in the outer heliosphere at a distance of about 90 AU, has been observed since July 2002 until recently (February 2003). This behavior can be interpreted as a possible manifestation of a combination of the global heliospheric disturbance produced by solar activity and the precursor of the outer heliosphere with its termination shock. The extremely large variability of the enhanced ion fluxes since the second half of 2002 in several energy channels from 0.5 to several MeV/nucleon is presumed to be associated with the sources of their acceleration near the termination shock. The simultaneous increase in the flux of protons with energies above 70 MeV may result from the easier penetration of Galactic cosmic rays because of the reduction in modulation at the declining phase in the current solar cycle 23 after the maximum in 2000 and from an admixture of the anomalous component accelerated at the termination shock.