Recent studies show that the majority of blue straggler stars ( BSSs ) in old open clusters are formed through mass transfer from an evolved star onto a main-sequence companion , resulting in a BSS and white dwarf ( WD ) in a binary system . We present constraints on the mass transfer histories of two BSS-WD binaries in the open cluster NGC 188 , using WD temperatures and surface gravities measured with HST COS far-ultraviolet spectroscopy . Adopting a Gaia -based cluster distance of 1847 \pm 107 pc , we determine that one system , WOCS 4540 , formed through Case C mass transfer resulting in a CO-core white dwarf with T _ { \text { eff } } = 17000 ^ { +140 } _ { -200 } K and a \log g = 7.80 ^ { +0.06 } _ { -0.06 } , corresponding to a mass of 0.53 ^ { +0.03 } _ { -0.03 } M _ { \odot } and a cooling age of 105 ^ { +6 } _ { -5 } Myr . The other system , WOCS 5379 , formed through Case B mass transfer resulting in a He-core white dwarf with T _ { \text { eff } } = 15500 ^ { +170 } _ { -150 } K and a \log g = 7.50 ^ { +0.06 } _ { -0.05 } , corresponding to a mass of 0.42 ^ { +0.02 } _ { -0.02 } M _ { \odot } and an age of 250 ^ { +20 } _ { -20 } Myr . The WD parameters are consistent across four different cluster distance assumptions . We determine possible progenitor binary systems with a grid of accretion models using MESA , and investigate whether these systems would lead to stable or unstable mass transfer . WOCS 4540 likely resulted from stable mass transfer during periastron passage in an eccentric binary system , while WOCS 5379 challenges our current understanding of the expected outcomes for mass transfer from red giant branch stars . Both systems are examples of the value in using detailed analyses to fine-tune our physical understanding of binary evolutionary processes .