We study dissociative electron attachment to furan (FN) (C(4)H(4)O), tetrahydrofuran (THF) (C(4)H(8)O), and fructose (FRU) (C(6)H(12)O(6)) using crossed electron/molecular beams experiments with mass spectrometric detection of the anions. We find that FN and THF are weak electron scavengers and subjected to dissociative electron attachment essentially in the energy range above 5.5 eV via core excited resonances. In striking contrast to that, FRU is very sensitive towards low energy electrons generating a variety of fragment ions via a pronounced low energy feature close to 0 eV. These reactions are associated with the degradation of the ring structure and demonstrate that THF cannot be used as surrogate to model deoxyribose in DNA with respect to the attack of electrons at subexcitation energies (<3 eV). The results support the picture that in DNA the sugar moiety itself is an active part in the initial molecular processes leading to single strand breaks.